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University Physics with Modern Physics In SI Units

Hugh D Young; Roger A Freedman

Chapter 2

Motion Along a Straight Line - all with Video Answers

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Chapter Questions

01:05

Problem 1

A car travels in the $+x$ -direction on a straight and level road. For the first $4.00 \mathrm{~s}$ of its motion, the average velocity of the car is $v_{\mathrm{av}-\mathrm{x}}=6.25 \mathrm{~m} / \mathrm{s}$. How far does the car travel in $4.00 \mathrm{~s}$ ?

Johnny Greavu
Johnny Greavu
University of Minnesota - Twin Cities
01:05

Problem 1

A car travels in the $+x$ -direction on a straight and level road. For the first $4.00 \mathrm{~s}$ of its motion, the average velocity of the car is $v_{\mathrm{av}-\mathrm{x}}=6.25 \mathrm{~m} / \mathrm{s}$. How far does the car travel in $4.00 \mathrm{~s}$ ?

Johnny Greavu
Johnny Greavu
University of Minnesota - Twin Cities
03:04

Problem 2

In an experiment, a shearwater (a seabird) was taken from its nest, flown $5150 \mathrm{~km}$ away, and released. The bird found its way back to its nest 13.5 days after release. If we place the origin at the nest and extend the $+x$ -axis to the release point, what was the bird's average velocity in $\mathrm{m} / \mathrm{s}$ (a) for the return flight and
(b) for the whole episode, from leaving the nest to returning?

Zachary Warner
Zachary Warner
Numerade Educator
02:43

Problem 3

You normally drive from Glasgow to Edinburgh via $\mathrm{M} 8$ motorway at an average speed of $72 \mathrm{~km} / \mathrm{h}$, and the trip takes $1 \mathrm{~h}$ and $2 \mathrm{~min}$. At peak times, however, heavy traffic slows you down and you drive the same distance at an average speed of only $49 \mathrm{~km} / \mathrm{h}$. How much longer does the trip take?

Nishant Kumar
Nishant Kumar
Numerade Educator
View

Problem 4

Starting from a pillar, you run $200 \mathrm{~m}$ east (the $+x$ -direction) at an average speed of $5.0 \mathrm{~m} / \mathrm{s}$ and then run $280 \mathrm{~m}$ west at an average speed of $4.0 \mathrm{~m} / \mathrm{s}$ to a post. Calculate (a) your average speed from pillar to post and (b) your average velocity from pillar to post.

Susan Hallstrom
Susan Hallstrom
Numerade Educator
02:04

Problem 5

Starting from the front door of a farmhouse, you walk $60.0 \mathrm{~m}$ due east to a windmill, turn around, and then slowly walk $40.0 \mathrm{~m}$ west to a bench, where you sit and watch the sunrise. It takes you $28.0 \mathrm{~s}$ to walk from the house to the windmill and then $36.0 \mathrm{~s}$ to walk from the windmill to the bench. For the entire trip from the front door to the bench, what are your (a) average velocity and (b) average speed?

Melissa Walsh
Melissa Walsh
Numerade Educator
04:27

Problem 6

A Honda Civic travels in a straight line along a road. The car's distance $x$ from a stop sign is given as a function of time $t$ by the equation $x(t)=\alpha t^{2}-\beta t^{3},$ where $\alpha=1.50 \mathrm{~m} / \mathrm{s}^{2}$ and
$\beta=0.0500 \mathrm{~m} / \mathrm{s}^{3} .$ Calculate the average velocity of the car for each time interval: (a) $t=0$ to $t=2.00 \mathrm{~s} ;$ (b) $t=0$ to $t=4.00 \mathrm{~s}$;
(c) $t=2.00 \mathrm{~s}$ to $t=4.00 \mathrm{~s}$.

Johnny Greavu
Johnny Greavu
University of Minnesota - Twin Cities
07:34

Problem 7

A car is stopped at a traffic light. It then travels along a straight road such that its distance from the light is given by $x(t)=b t^{2}-c t^{3},$ where $b=2.40 \mathrm{~m} / \mathrm{s}^{2}$ and $c=0.120 \mathrm{~m} / \mathrm{s}^{3}$.
(a) Calculate the average velocity of the car for the time interval $t=0$ to $t=10.0 \mathrm{~s}$. (b) Calculate the instantaneous velocity of the car at $t=0, t=5.0 \mathrm{~s}$, and $t=10.0 \mathrm{~s}$. (c) How long after starting from rest is the car again at rest?

CA
Chi-Chung Ai
Numerade Educator
01:16

Problem 8

A bird is flying due east. Its distance from a tall building is given by $x(t)=28.0 \mathrm{~m}+(12.4 \mathrm{~m} / \mathrm{s}) t-\left(0.0450 \mathrm{~m} / \mathrm{s}^{3}\right) t^{3} .$ What is the instantaneous velocity of the bird when $t=8.00 \mathrm{~s}$ ?

Dominador Tan
Dominador Tan
Numerade Educator
05:03

Problem 9

A ball moves in a straight line (the $x$ -axis). The graph in Fig. E2.9 shows this ball's velocity as a function of time. (a) What are the ball's average speed and average velocity during the first $3.0 \mathrm{~s} ?$
(b) Suppose that the ball moved in such a way that the graph segment after $2.0 \mathrm{~s}$ was $-3.0 \mathrm{~m} / \mathrm{s}$ instead of $+3.0 \mathrm{~m} / \mathrm{s}$. Find the ball's average speed and average velocity in this case.

João Gabriel Alencar Caribé
João Gabriel Alencar Caribé
Numerade Educator
View

Problem 10

A physics professor leaves her house and walks along the pavement toward campus. After 5 min it starts to rain, and she returns home. Her distance from her house as a function of time is shown in Fig. E2.10. At which of the labeled points is her velocity
(a) zero?
(b) constant and positive?
(c) constant and negative?
(d) increasing in magnitude? (e) decreasing in magnitude?

Gregory Devenport
Gregory Devenport
Numerade Educator
03:05

Problem 11

A test car travels in a straight line along the $x$ -axis. The graph in Fig. E2.11 shows the car's position $x$ as a function of time. Find its instantaneous velocity at points $A$ through $G$.

Ryan Hood
Ryan Hood
Numerade Educator
02:23

Problem 12

Figure E2.12 shows the velocity of a solar-powered car as a function of time. The driver accelerates from a stop sign, cruises for $20 \mathrm{~s}$ at a constant speed of $60 \mathrm{~km} / \mathrm{h}$, and then brakes to come to a stop 40 s after leaving the stop sign. (a) Compute the average acceleration during these time intervals: (i) $t=0$ to $t=10 \mathrm{~s}$;
(ii) $t=30 \mathrm{~s}$ to
$t=40 \mathrm{~s} ;$ (iii) $t=10 \mathrm{~s}$ to $t=30 \mathrm{~s} ;$ (iv) $t=0$ to $t=40 \mathrm{~s}$. (b) What is
the instantaneous acceleration at $t=20 \mathrm{~s}$ and at $t=35 \mathrm{~s}$ ?

GL
Gilbert Lopez
University of California, Berkeley
11:04

Problem 13

A turtle crawls along a straight line, which we'll call the $x$ -axis with the positive direction to the right. The equation for the turtle's position as a function of time is $x(t)=50.0 \mathrm{~cm}+$ $(2.00 \mathrm{~cm} / \mathrm{s}) t-\left(0.0625 \mathrm{~cm} / \mathrm{s}^{2}\right) t^{2}$. (a) Find the turtle's initial velocity,
initial position, and initial acceleration. (b) At what time $t$ is the velocity of the turtle zero? (c) How long after starting does it take the turtle to return to its starting point? (d) At what times $t$ is the turtle a distance of $10.0 \mathrm{~cm}$ from its starting point? What is the velocity (magnitude and direction) of the turtle at each of those times? (e) Sketch graphs of $x$ versus $t, v_{x}$ versus $t,$ and $a_{x}$ versus $t,$ for the time interval $t=0$ to $t=40 \mathrm{~s}$.

Ryan Hood
Ryan Hood
Numerade Educator
02:05

Problem 14

A race car starts from rest and travels east along a straight and level track. For the first $5.0 \mathrm{~s}$ of the car's motion, the eastward component of the car's velocity is given by $v_{x}(t)=\left(0.860 \mathrm{~m} / \mathrm{s}^{3}\right) t^{2}$. What is the acceleration of the car when $v_{x}=12.0 \mathrm{~m} / \mathrm{s} ?$

Johnny Greavu
Johnny Greavu
University of Minnesota - Twin Cities
03:40

Problem 15

A car's velocity as a function of time is given by $v_{x}(t)=\alpha+\beta t^{2}, \quad$ where $\quad \alpha=3.00 \mathrm{~m} / \mathrm{s} \quad$ and $\quad \beta=0.100 \mathrm{~m} / \mathrm{s}^{3}$
(a) Calculate the average acceleration for the time interval $t=0$ to $t=5.00 \mathrm{~s}$. (b) Calculate the instantaneous acceleration for $t=0$ and $t=5.00 \mathrm{~s}$. (c) Draw $v_{x}-t$ and $a_{x}-t$ graphs for the car's motion between $t=0$ and $t=5.00 \mathrm{~s}$.

Ryan Hood
Ryan Hood
Numerade Educator
04:44

Problem 16

An astronaut has left the International Space Station to test a new space scooter. Her partner measures the following velocity changes, each taking place in a $10 \mathrm{~s}$ interval. What are the magnitude, the algebraic sign, and the direction of the average acceleration in each interval? Assume that the positive direction is to the right. (a) At the beginning of the interval, the astronaut is moving toward the right along the $x$ -axis at $15.0 \mathrm{~m} / \mathrm{s}$, and at the end of the interval she is moving toward the right at $5.0 \mathrm{~m} / \mathrm{s}$. (b) At the beginning she is moving toward the left at $5.0 \mathrm{~m} / \mathrm{s}$ and at the end she is moving toward the left at $15.0 \mathrm{~m} / \mathrm{s}$. (c) At the beginning she is moving toward the right at $15.0 \mathrm{~m} / \mathrm{s}$, and at the end she is moving toward the left at $15.0 \mathrm{~m} / \mathrm{s}$.

Johnny Greavu
Johnny Greavu
University of Minnesota - Twin Cities
03:09

Problem 17

The position of the front bumper of a test car under microprocessor control is given by $x(t)=2.17 \mathrm{~m}+\left(4.80 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2}-$
$\left(0.100 \mathrm{~m} / \mathrm{s}^{6}\right) t^{6} .$ (a) Find its position and acceleration at the instants when the car has zero velocity. (b) Draw $x-t, v_{x}-t,$ and $a_{x}-t$ graphs for the motion of the bumper between $t=0$ and $t=2.00 \mathrm{~s}$.

Justin Swantek
Justin Swantek
Numerade Educator
02:48

Problem 18

Estimate the distance that your car travels on the entrance ramp to a freeway as it accelerates from $50 \mathrm{~km} / \mathrm{h}$ to the freeway speed of $110 \mathrm{~km} / \mathrm{h}$. During this motion what is the average acceleration of the car?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:41

Problem 19

An antelope moving with constant acceleration covers the distance between two points $70.0 \mathrm{~m}$ apart in $6.00 \mathrm{~s}$. Its speed as it passes the second point is $15.0 \mathrm{~m} / \mathrm{s}$. What are (a) its speed at the first point and
(b) its acceleration?

Sheh Lit Chang
Sheh Lit Chang
University of Washington
02:52

Problem 20

A Tennis Serve. In the fastest measured tennis serve, the ball left the racquet at $73.14 \mathrm{~m} / \mathrm{s}$. A served tennis ball is typically in contact with the racquet for $30.0 \mathrm{~ms}$ and starts from rest. Assume constant acceleration. (a) What was the ball's acceleration during this serve? (b) How far did the ball travel during the serve?

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
01:43

Problem 21

The fastest measured pitched baseball left the pitcher's hand at a speed of $45.0 \mathrm{~m} / \mathrm{s}$. If the pitcher was in contact with the ball over a distance of $1.50 \mathrm{~m}$ and produced constant acceleration,
(a) what acceleration did he give the ball, and
(b) how much time did it take him to pitch it?

Ryan Hood
Ryan Hood
Numerade Educator
01:49

Problem 22

You are traveling on a motorway at the posted speed limit of $110 \mathrm{~km} / \mathrm{h}$ when you see that the traffic in front of you has stopped due to an accident up ahead. You step on your brakes to slow down as quickly as possible. (a) Estimate how many seconds it takes you to slow down to $50 \mathrm{~km} / \mathrm{h}$. What is the magnitude of the average acceleration of the car while it is slowing down? With this same average acceleration, (b) how much longer would it take you to stop, and (c) what total distance would you travel from when you first apply the brakes until the car stops?

Dominador Tan
Dominador Tan
Numerade Educator
02:24

Problem 23

The human body can survive an acceleration trauma incident (sudden stop) if the magnitude of the acceleration is less than $250 \mathrm{~m} / \mathrm{s}^{2}$. If you are in an automobile accident with an initial speed of $105 \mathrm{~km} / \mathrm{h}$ and are stopped by an airbag that inflates from the dashboard, over what minimum distance must the airbag stop you for you to survive the crash?

Melissa Walsh
Melissa Walsh
Numerade Educator
View

Problem 24

A car sits on an entrance ramp to a freeway, waiting for a break in the traffic. Then the driver accelerates with constant acceleration along the ramp and onto the freeway. The car starts from rest, moves in a straight line, and has a speed of $20 \mathrm{~m} / \mathrm{s}$ when it reaches the end of the 120 -m-long ramp.
(a) What is the acceleration of the car? (b) How much time does it take the car to travel the length of the ramp? (c) The traffic on the freeway is moving at a constant speed of $20 \mathrm{~m} / \mathrm{s}$. What distance does the traffic travel while the car is moving the length of the ramp?

Jaclyn Bastardi
Jaclyn Bastardi
Numerade Educator
04:00

Problem 25

During an auto accident, the vehicle's airbags deploy and slow down the passengers more gently than if they had hit the windshield or steering wheel. According to safety standards, airbags produce a maximum acceleration of $60 \mathrm{~g}$ that lasts for only $36 \mathrm{~ms}$ (or less). How far (in meters) does a person travel in coming to a complete stop in $36 \mathrm{~ms}$ at a constant acceleration of $60 \mathrm{~g}$ ?

CA
Chi-Chung Ai
Numerade Educator
08:17

Problem 26

A cat walks in a straight line, which we shall call the $x$ -axis, with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time (Fig. E2.26). (a) Find the cat's velocity at $t=4.0 \mathrm{~s}$ and at $t=7.0 \mathrm{~s}$. (b) What is the cat's acceleration at $t=3.0 \mathrm{~s}$ ? At $t=6.0 \mathrm{~s}$ ? At $t=7.0 \mathrm{~s} ?$ (c) What distance does the cat move during the first $4.5 \mathrm{~s}$ ? From $t=0$ to $t=7.0 \mathrm{~s}$ ? (d) Assuming that the cat started at the origin, sketch clear graphs of the cat's acceleration and position as functions of time.

CA
Chi-Chung Ai
Numerade Educator
View

Problem 27

It has been suggested, and not facetiously, that life might have originated on Mars and been carried to the earth when a meteor hit Mars and blasted pieces of rock (perhaps containing primitive life) free of the Martian surface. Astronomers know that many Martian rocks have come to the earth this way. (For instance, search the Internet for "ALH 84001 .") One objection to this idea is that microbes would have had to undergo an enormous lethal acceleration during the impact. Let us investigate how large such an acceleration might be. To escape Mars, rock fragments would have to reach its escape velocity of $5.0 \mathrm{~km} / \mathrm{s}$, and that would most likely happen over a distance of about $4.0 \mathrm{~m}$ during the meteor impact. (a) What would be the acceleration (in $\mathrm{m} / \mathrm{s}^{2}$ and $g$ 's) of such a rock fragment, if the acceleration is constant? (b) How long would this acceleration last? (c) In tests, scientists have found that over $40 \%$ of Bacillus subtilis bacteria survived after an acceleration of $450,000 g$. In light of your answer to part (a), can we rule out the hypothesis that life might have been blasted from Mars to the earth?

Jaclyn Bastardi
Jaclyn Bastardi
Numerade Educator
01:26

Problem 28

Two cars, $A$ and $B$, move along the $x$ -axis. Figure $\mathbf{E} 2.28$ is a graph of the positions of $A$ and $B$ versus time. (a) In motion diagrams (like Figs. $2.13 \mathrm{~b}$ and $2.14 \mathrm{~b}$ ), show the position, velocity, and acceleration of each of the two cars at $t=0, t=1 \mathrm{~s},$ and $t=3 \mathrm{~s}$. (b) At what time(s), if any, do $A$ and $B$ have the same position?
(c) Graph velocity versus time for both $A$ and $B$. (d) At what time(s), if any, do $A$ and $B$ have the same velocity?
(e) At what time(s), if any, does car $A$ pass car $B ?$ (f) At what time(s), if any, does car $B$ pass car $A$ ?

Dominador Tan
Dominador Tan
Numerade Educator
06:59

Problem 29

The graph in Fig. E2.29 shows the velocity of a motorcycle police officer plotted as a function of time. (a) Find the instantaneous acceleration at $t=3 \mathrm{~s}, t=7 \mathrm{~s},$ and $t=11 \mathrm{~s}$. (b) How far does the officer go in the first $5 \mathrm{~s}$ ? The first $9 \mathrm{~s}$ ? The first $13 \mathrm{~s}$ ?

Ryan Hood
Ryan Hood
Numerade Educator
03:04

Problem 30

A small block has constant acceleration as it slides down a frictionless incline. The block is released from rest at the top of the incline, and its speed after it has traveled $6.80 \mathrm{~m}$ to the bottom of the incline is $3.80 \mathrm{~m} / \mathrm{s}$. What is the speed of the block when it is $3.40 \mathrm{~m}$ from the top of the incline?

Ryan Hood
Ryan Hood
Numerade Educator
02:51

Problem 31

(a) If a flea can jump straight up to a height of $0.440 \mathrm{~m}$, what is its initial speed as it leaves the ground? (b) How long is it in the air?

Zachary Warner
Zachary Warner
Numerade Educator
03:57

Problem 32

A small rock is thrown vertically upward with a speed of $22.0 \mathrm{~m} / \mathrm{s}$ from the edge of the roof of a $30.0-\mathrm{m}$ -tall building. The rock doesn't hit the building on its way back down and lands on the street below. Ignore air resistance. (a) What is the speed of the rock just before it hits the street? (b) How much time elapses from when the rock is thrown until it hits the street?

Johnny Greavu
Johnny Greavu
University of Minnesota - Twin Cities
01:30

Problem 33

A juggler throws a bowling pin straight up with an initial speed of $8.20 \mathrm{~m} / \mathrm{s}$. How much time elapses until the bowling pin returns to the juggler's hand?

Ryan Hood
Ryan Hood
Numerade Educator
03:01

Problem 34

You throw a glob of putty straight up toward the ceiling, which is $3.60 \mathrm{~m}$ above the point where the putty leaves your hand. The initial speed of the putty as it leaves your hand is $9.50 \mathrm{~m} / \mathrm{s}$. (a) What is the speed of the putty just before it strikes the ceiling?
(b) How much time from when it leaves your hand does it take the putty to reach the ceiling?

Nishant Kumar
Nishant Kumar
Numerade Educator
00:01

Problem 35

A tennis ball on Mars, where the acceleration due to gravity is $0.379 g$ and air resistance is negligible, is hit directly upward and returns to the same level $8.5 \mathrm{~s}$ later. (a) How high above its original point did the ball go? (b) How fast was it moving just after it was hit? (c) Sketch graphs of the ball's vertical position, vertical velocity, and vertical acceleration as functions of time while it's in the Martian air.

Susan Hallstrom
Susan Hallstrom
Numerade Educator
02:12

Problem 36

Estimate the maximum height that you can throw a tennis ball straight up. (a) For this height, how long after the ball leaves your hand does it return to your hand? (b) Estimate the distance that the ball moves while you are throwing it- that is, the distance from where the ball is when you start your throw until it leaves your hand. Calculate the average acceleration in $\mathrm{m} / \mathrm{s}^{2}$ that the ball has while it is being thrown, as it moves from rest to the point where it leaves your hand.

Dominador Tan
Dominador Tan
Numerade Educator
03:52

Problem 37

A rock is thrown straight up with an initial speed of $24.0 \mathrm{~m} / \mathrm{s}$ Neglect air resistance.
(a) At $t=1.0 \mathrm{~s}$, what are the directions of the velocity and acceleration of the rock? Is the speed of the rock increasing or decreasing? (b) At $t=3.0 \mathrm{~s}$, what are the directions of the velocity and acceleration of the rock? Is the speed of the rock increasing or decreasing?

CA
Chi-Chung Ai
Numerade Educator
05:16

Problem 38

A brick is dropped (zero initial speed) from the roof of a building. The brick strikes the ground in $1.90 \mathrm{~s}$. You may ignore air resistance, so the brick is in free fall. (a) How tall, in meters, is the building? (b) What is the magnitude of the brick's velocity just before it reaches the ground? (c) Sketch $a_{y}-t, v_{y}-t,$ and $y-t$ graphs for the motion of the brick.

Johnny Greavu
Johnny Greavu
University of Minnesota - Twin Cities
02:26

Problem 39

A meter stick is held vertically above your hand, with the lower end between your thumb and first finger. When you see the meter stick released, you grab it with those two fingers. You can calculate your reaction time from the distance the meter stick falls, read directly from the point where your fingers grabbed it. (a) Derive a relationship for your reaction time in terms of this measured distance, $d$. (b) If the measured distance is $17.6 \mathrm{~cm},$ what is your reaction time?

Ryan Hood
Ryan Hood
Numerade Educator
01:48

Problem 40

A lunar lander is making its descent to Moon Base I (Fig. E2.40). The lander descends slowly under the retro-thrust of its descent engine. The engine is cut off when the lander is $5.0 \mathrm{~m}$ above the surface and has a downward speed of $0.8 \mathrm{~m} / \mathrm{s} .$ With the engine off, the lander is in free fall. What is the speed of the lander just before it touches the surface? The acceleration due to gravity on the moon is $1.6 \mathrm{~m} / \mathrm{s}^{2}$

Johnny Greavu
Johnny Greavu
University of Minnesota - Twin Cities
01:47

Problem 40

A lunar lander is making its descent te Moon Base I (Fig. E2.40). The lander descends slowly under the retro-thrust of its descent engine. The engine is cut off when the lander is $5.0 \mathrm{~m}$ above the surface and has a downward speed of $0.8 \mathrm{~m} / \mathrm{s}$. With the engine off, the lander is in free fall. What is the speed of the lander just before it touches the surface? The acceleration due to gravity on the moon is $1.6 \mathrm{~m} / \mathrm{s}^{2}$.

Melissa Walsh
Melissa Walsh
Numerade Educator
11:06

Problem 41

A $7500 \mathrm{~kg}$ rocket blasts off vertically from the launch pad with a constant upward acceleration of $2.25 \mathrm{~m} / \mathrm{s}^{2}$ and feels no appreciable air resistance. When it has reached a height of $525 \mathrm{~m}$, its engines suddenly fail; the only force acting on it is now gravity.
(a) What is the maximum height this rocket will reach above the launch pad?
(b) How much time will elapse after engine failure before the rocket comes crashing down to the launch pad, and how fast will it be moving just before it crashes? (c) Sketch $a_{y}-t, v_{y}-t,$ and $y-t$ graphs of the rocket's motion from the instant of blast-off to the instant just before it strikes the launch pad.

Ryan Hood
Ryan Hood
Numerade Educator
05:30

Problem 42

A hot-air balloonist, rising vertically with a constant velocity of magnitude $5.00 \mathrm{~m} / \mathrm{s}$, releases a sandbag at an instant when the balloon is $40.0 \mathrm{~m}$ above the ground (Fig. E2.42). After the sandbag is released, it is in free fall.
(a) Compute the position and velocity of the sandbag at $0.250 \mathrm{~s}$ and $1.00 \mathrm{~s}$ after its release. (b) How many seconds after its release does the bag strike the ground? (c) With what magnitude of velocity does it strike the ground? (d) What is the greatest height above the ground that the sandbag reaches? (e) Sketch $a_{y}-t, v_{y}-t,$ and $y-t$ graphs for the motion.

Johnny Greavu
Johnny Greavu
University of Minnesota - Twin Cities
03:04

Problem 43

You throw a rock straight up and find that it returns to your hand $3.60 \mathrm{~s}$ after it left your hand. Neglect air resistance. What was the maximum height above your hand that the rock reached?

CA
Chi-Chung Ai
Numerade Educator
04:35

Problem 44

An egg is thrown nearly vertically upward from a point near the cornice of a tall building. The egg just misses the cornice on the way down and passes a point $30.0 \mathrm{~m}$ below its starting point $5.00 \mathrm{~s}$ after it leaves the thrower's hand. Ignore air resistance.
(a) What is the initial speed of the egg? (b) How high does it rise above its starting point?
(c) What is the magnitude of its velocity at the highest point?
(d) What are the magnitude and direction of its acceleration at the highest point?
(e) Sketch $a_{y}-t, v_{y}-t,$ and $y-t$ graphs for the motion of the egg.

Johnny Greavu
Johnny Greavu
University of Minnesota - Twin Cities
02:59

Problem 45

A A $15 \mathrm{~kg}$ rock is dropped from rest on the earth and reaches the ground in $1.75 \mathrm{~s}$. When it is dropped from the same height on Saturn's satellite Enceladus, the rock reaches the ground in $18.6 \mathrm{~s}$. What is the acceleration due to gravity on Enceladus?

Melissa Walsh
Melissa Walsh
Numerade Educator
03:53

Problem 46

A large boulder is ejected vertically upward from a volcano with an initial speed of $40.0 \mathrm{~m} / \mathrm{s}$. Ignore air resistance. (a) At what time after being ejected is the boulder moving at $20.0 \mathrm{~m} / \mathrm{s}$ upward? (b) At what time is it moving at $20.0 \mathrm{~m} / \mathrm{s}$ downward? (c) When is the displacement of the boulder from its initial position zero? (d) When is the velocity of the boulder zero? (e) What are the magnitude and direction of the acceleration while the boulder is (i) moving upward?
(ii) Moving downward? (iii) At the highest point? (f) Sketch $a_{y}-t, v_{y}-t,$ and $y-t$ graphs for the motion.

Johnny Greavu
Johnny Greavu
University of Minnesota - Twin Cities
03:03

Problem 47

You throw a small rock straight up from the edge of a bridge that crosses a river. The rock passes you on its way down, $6.00 \mathrm{~s}$ after it was thrown. What is the speed of the rock just before it reaches the water $28.0 \mathrm{~m}$ below the point where the rock left your hand? Ignore air resistance.

Melissa Walsh
Melissa Walsh
Numerade Educator
04:39

Problem 48

Consider the motion described by the $v_{x}-t$ graph of Fig. E2.26.
(a) Calculate the area under the graph between $t=0$ and $t=6.0 \mathrm{~s}$.
(b) For the time interval $t=0$ to $t=6.0 \mathrm{~s}$, what is the magnitude of the average velocity of the cat? (c) Use constant-acceleration equations to calculate the distance the cat travels in this time interval. How does your result compare to the area you calculated in part (a)?

CA
Chi-Chung Ai
Numerade Educator
03:27

Problem 49

A rocket starts from rest and moves upward from the surface of the earth. For the first $10.0 \mathrm{~s}$ of its motion, the vertical acceleration of the rocket is given by $a_{y}=\left(2.80 \mathrm{~m} / \mathrm{s}^{3}\right) t,$ where the $+y$ -direction is upward. (a) What is the height of the rocket above the surface of the earth at $t=10.0 \mathrm{~s} ?$ (b) What is the speed of the rocket when it is $325 \mathrm{~m}$ above the surface of the earth?

Ryan Hood
Ryan Hood
Numerade Educator
02:30

Problem 50

A small object moves along the $x$ -axis with acceleration $a_{x}(t)=-\left(0.0320 \mathrm{~m}/ \mathrm{s}^{3}\right)(15.0 \mathrm{~s}-t) .$ At $t=0$ the object is at
$x=-14.0 \mathrm{~m}$ and has velocity $v_{0 x}=8.00 \mathrm{~m} / \mathrm{s}$. What is the $x$ -coordinate of the object when $t=10.0 \mathrm{~s} ?$

Johnny Greavu
Johnny Greavu
University of Minnesota - Twin Cities
View

Problem 51

The acceleration of a motorcycle is given by $a_{x}(t)=A t-B t^{2},$ where $A=1.50 \mathrm{~m} / \mathrm{s}^{3}$ and $B=0.120 \mathrm{~m} / \mathrm{s}^{4}$. The
(a) Find its position and vemotorcycle is at rest at the origin at time $t=0$. locity as functions of time. (b) Calculate the maximum velocity it attains.

Jaclyn Bastardi
Jaclyn Bastardi
Numerade Educator
View

Problem 52

The acceleration of a bus is given by $a_{x}(t)=\alpha t,$ where $\alpha=1.2 \mathrm{~m} / \mathrm{s}^{3} .$ (a) If the bus's velocity at time $t=1.0 \mathrm{~s}$ is $5.0 \mathrm{~m} / \mathrm{s},$ what is its velocity at time $t=2.0 \mathrm{~s} ?(\mathrm{~b})$ If the bus's position at time $t=1.0 \mathrm{~s}$ is $6.0 \mathrm{~m},$ what is its position at time $t=2.0 \mathrm{~s} ?$ (c) Sketch $a_{y}-t, v_{y}-t,$ and $x-t$ graphs for the motion.

Jaclyn Bastardi
Jaclyn Bastardi
Numerade Educator
02:30

Problem 53

A typical male sprinter can maintain his maximum acceleration for $2.0 \mathrm{~s}$, and his maximum speed is $10 \mathrm{~m} / \mathrm{s}$. After he reaches this maximum speed, his acceleration becomes zero, and then he runs at constant speed. Assume that his acceleration is constant during the first $2.0 \mathrm{~s}$ of the race, that he starts from rest, and that he runs in a straight line. (a) How far has the sprinter run when he reaches his maximum speed? (b) What is the magnitude of his average velocity for a race of
(ii) $100.0 \mathrm{~m} ;$
(iii) $200.0 \mathrm{~m} ?$
these lengths: (i) $50.0 \mathrm{~m} ;$

Dominador Tan
Dominador Tan
Numerade Educator
03:47

Problem 54

A lunar lander is descending toward the moon's surface. Until the lander reaches the surface, its height above the surface of the moon is given by $y(t)=b-c t+d t^{2},$ where $b=800 \mathrm{~m}$ is the initial height of the lander above the surface, $c=60.0 \mathrm{~m} / \mathrm{s}$, and $d=1.05 \mathrm{~m} / \mathrm{s}^{2}$
(a) What is the initial velocity of the lander, at $t=0 ?(b)$ What is the velocity of the lander just before it reaches the lunar surface?

Zachary Warner
Zachary Warner
Numerade Educator
03:36

Problem 55

Earthquakes produce several types of shock waves. The most well known are the P-waves (P for primary or pressure) and the S-waves (S for secondary or shear). In the earth's crust, P-waves travel at about $6.5 \mathrm{~km} / \mathrm{s}$ and S-waves move at about $3.5 \mathrm{~km} / \mathrm{s}$. The time delay between the arrival of these two waves at a seismic recording station tells geologists how far away an earthquake occurred. If the time delay is $33 \mathrm{~s}$, how far from the seismic station did the earthquake occur?

Ryan Hood
Ryan Hood
Numerade Educator
01:31

Problem 56

You throw a small rock straight up with initial speed $V_{0}$ from the edge of the roof of a building that is a distance $H$ above the ground. The rock travels upward to a maximum height in time $T_{\max },$ misses the edge of the roof on its way down, and reaches the ground in time $T_{\text {total }}$ after it was thrown. Neglect air resistance. If the total time the rock is in the air is three times the time it takes it to reach its maximum height, so $T_{\text {total }}=3 T_{\max },$ then in terms of $H$ what must be the value of $V_{0} ?$

Dominador Tan
Dominador Tan
Numerade Educator
02:19

Problem 57

A rocket carrying a satellite is accelerating straight up from the earth's surface. At $1.15 \mathrm{~s}$ after liftoff, the rocket clears the top of its launch platform, $63 \mathrm{~m}$ above the ground. After an additional $4.75 \mathrm{~s}$, it is $1.00 \mathrm{~km}$ above the ground. Calculate the magnitude of the average velocity of the rocket for (a) the $4.75 \mathrm{~s}$ part of its flight and $(b)$ the first $5.90 \mathrm{~s}$ of its flight.

Zachary Warner
Zachary Warner
Numerade Educator
02:22

Problem 58

A block moving on a horizontal surface is at $x=0$ when $t=0$ and is sliding east with a speed of $12.0 \mathrm{~m} / \mathrm{s}$. Because of a net force acting on the block. it has a constant acceleration with direction west and magnitude $2.00 \mathrm{~m} / \mathrm{s}^{2}$. The block travels east, slows down, reverses direction, and then travels west with increasing speed.
(a) At what value of $t$ is the block again at $x=0 ?$ (b) What is the maximum distance east of $x=0$ that the rock reaches, and how long does it take the rock to reach this point?

Dominador Tan
Dominador Tan
Numerade Educator
04:02

Problem 59

A block is sliding with constant acceleration down an incline. The block starts from rest at $t=0$ and has speed $3.00 \mathrm{~m} / \mathrm{s}$ after it has traveled a distance $8.00 \mathrm{~m}$ from its starting point. (a) What is the speed of the block when it is a distance of $16.0 \mathrm{~m}$ from its $t=0$ starting point? (b) How long does it take the block to slide $16.0 \mathrm{~m}$ from its starting point?

CA
Chi-Chung Ai
Numerade Educator
04:59

Problem 60

An underground train starts from rest at a station and accelerates at a rate of $1.60 \mathrm{~m} / \mathrm{s}^{2}$ for $14.0 \mathrm{~s}$. It runs at constant speed for 70.0 s and slows down at a rate of $3.50 \mathrm{~m} / \mathrm{s}^{2}$ until it stops at the next station. Find the total distance covered.

Melissa Walsh
Melissa Walsh
Numerade Educator
09:52

Problem 61

A gazelle is running in a straight line (the $x$ -axis). The graph in Fig. $\mathbf{P} 2.61$ shows this animal's velocity as a function of time. During the first $12.0 \mathrm{~s}$, find (a) the total distance moved and (b) the displacement of the gazelle. (c) Sketch an $a_{x}-t$ graph showing this gazelle's acceleration as a function of time for the first $12.0 \mathrm{~s}$.

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
06:52

Problem 62

The engineer of a passenger train traveling at $25.0 \mathrm{~m} / \mathrm{s}$ sights a freight train whose caboose is $200 \mathrm{~m}$ ahead on the same track (Fig. $\mathbf{P} 2.62$ ). The freight train is traveling at $15.0 \mathrm{~m} / \mathrm{s}$ in the same direction as the passenger train. The engineer of the passenger train immediately applies the brakes, causing a constant acceleration of $0.100 \mathrm{~m} / \mathrm{s}^{2}$ in a direction opposite to the train's velocity, while the freight train continues with constant speed. Take $x=0$ at the location of the front of the passenger train when the engineer applies the brakes.
(a) Will the cows nearby witness a collision?
(b) If so, where will it take place? (c) On a single graph, sketch the positions of the front of the passenger train and the back of the freight train.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
02:47

Problem 63

A ball starts from rest and rolls down a hill with uniform acceleration, traveling $200 \mathrm{~m}$ during the second $5.0 \mathrm{~s}$ of its motion. How far did it roll during the first $5.0 \mathrm{~s}$ of motion?

Ryan Hood
Ryan Hood
Numerade Educator
08:20

Problem 64

A rock moving in the $+x$ -direction with speed $16.0 \mathrm{~m} / \mathrm{s}$ has a net force applied to it at time $t=0$, and this produces a constant acceleration in the $-x$ -direction that has magnitude $4.00 \mathrm{~m} / \mathrm{s}^{2}$. For what three times $t$ after the force is applied is the rock a distance of $24.0 \mathrm{~m}$ from its position at $t=0 ?$ For each of these three values of $t,$ what is the velocity (magnitude and direction) of the rock?

CA
Chi-Chung Ai
Numerade Educator
06:18

Problem 65

A car and a truck start from rest at the same instant, with the car initially at some distance behind the truck. The truck has a constant acceleration of $2.10 \mathrm{~m} / \mathrm{s}^{2},$ and the car has an acceleration of $3.40 \mathrm{~m} / \mathrm{s}^{2}$ The car overtakes the truck after the truck has moved $60.0 \mathrm{~m}$. (a) How much time does it take the car to overtake the truck? (b) How far was the car behind the truck initially? (c) What is the speed of each when they are abreast? (d) On a single graph, sketch the position of each vehicle as a function of time. Take $x=0$ at the initial location of the truck.

Ryan Hood
Ryan Hood
Numerade Educator
02:41

Problem 66

You are standing at rest at a bus stop. A bus moving a a constant speed of $5.00 \mathrm{~m} / \mathrm{s}$ passes you. When the rear of the bus is $12.0 \mathrm{~m}$ past you, you realize that it is your bus, so you start to run toward it with a constant acceleration of $0.960 \mathrm{~m} / \mathrm{s}^{2} .$ How far would you have to run before you catch up with the rear of the bus, and how fast must you be running then? Would an average college student be physically able to accomplish this?

Narayan Hari
Narayan Hari
Numerade Educator
04:04

Problem 67

A sprinter runs a $100 \mathrm{~m}$ dash in $12.0 \mathrm{~s}$. She starts from rest with a constant acceleration $a_{x}$ for $3.0 \mathrm{~s}$ and then runs with constant speed for the remainder of the race. What is the value of $a_{x} ?$

CA
Chi-Chung Ai
Numerade Educator
04:20

Problem 68

An object's velocity is measured to be $v_{x}(t)=\alpha-\beta t^{2},$ where $\alpha=4.00 \mathrm{~m} / \mathrm{s}$ and $\beta=2.00 \mathrm{~m} / \mathrm{s}^{3} .$ At $t=0$ the object is at $x=0$
(a) Calculate the object's position and acceleration as functions of time.
(b) What is the object's maximum positive displacement from the origin?

Zachary Warner
Zachary Warner
Numerade Educator
06:16

Problem 69

An object is moving along the $x$ -axis. At $t=0$ it is at $x=0 .$ Its $x$ -component of velocity $v_{x}$ as a function of time is given by $v_{x}(t)=\alpha t-\beta t^{3},$ where $\alpha=8.0 \mathrm{~m} / \mathrm{s}^{2}$ and $\beta=4.0 \mathrm{~m} / \mathrm{s}^{4} .$ (a) At what nonzero time $t$ is the object again at $x=0 ?$ (b) At the time calculated in part (a), what are the velocity and acceleration of the object (magnitude and direction)?

CA
Chi-Chung Ai
Numerade Educator
03:28

Problem 70

You are on the roof of the physics building, $46.0 \mathrm{~m}$ above the ground (Fig. $\mathbf{P} 2 . \mathbf{7 0}$ ). Your physics professor, who is $1.80 \mathrm{~m}$ tall, is walking alongside the building at a constant speed of $1.20 \mathrm{~m} / \mathrm{s}$. If you wish to drop an egg on your professor's head, where should the professor be when you release the egg? Assume that the egg is in free fall.

CA
Chi-Chung Ai
Numerade Educator
05:46

Problem 71

The acceleration of a particle is given by $a_{x}(t)=$ $-2.00 \mathrm{~m} / \mathrm{s}^{2}+\left(3.00 \mathrm{~m} / \mathrm{s}^{3}\right) t$
Find the initial velocity $v_{0 x}$ such that the particle will have the same $x$ coordinate at $t=4.00 \mathrm{~s}$ as it had at $t=0 .(b)$ What will be the velocity at $t=4.00 \mathrm{~s} ?$

Zachary Warner
Zachary Warner
Numerade Educator
10:06

Problem 72

A small rock is thrown straight up with initial speed $v_{0}$ from the edge of the roof of a building with height $H$. The rock travels upward and then downward to the ground at the base of the building. Let $+y$ be upward, and neglect air resistance.
(a) For the rock's motion from the roof to the ground, what is the vertical component $v_{\mathrm{av}-y}$ of its average velocity? Is this quantity positive or negative? Explain.
(b) What does your expression for $v_{\mathrm{av}-y}$ give in the limit that $H$ is zero? Explain.
(c) Show that your result in part
(a) agrees with Eq. (2.10) .

CA
Chi-Chung Ai
Numerade Educator
04:28

Problem 73

A watermelon is dropped from the edge of the roof of a building and falls to the ground. You are standing on the pavement and see the watermelon falling when it is $30.0 \mathrm{~m}$ above the ground. Then $1.50 \mathrm{~s}$ after you first spot it, the watermelon lands at your feet. What is the height of the building? Neglect air resistance.

Melissa Walsh
Melissa Walsh
Numerade Educator
02:35

Problem 74

A flowerpot falls off a windowsill and passes the window of the story below. Ignore air resistance. It takes the pot $0.380 \mathrm{~s}$ to pass from the top to the bottom of this window, which is $1.90 \mathrm{~m}$ high. How far is the top of the window below the windowsill from which the flowerpot fell?

Johnny Greavu
Johnny Greavu
University of Minnesota - Twin Cities
08:12

Problem 75

Kemal heaves a $7.26 \mathrm{~kg}$ shot straight up, giving it a constant upward acceleration from rest of $35.0 \mathrm{~m} / \mathrm{s}^{2}$ for $64.0 \mathrm{~cm} .$ He releases it $2.20 \mathrm{~m}$ above the ground. Ignore air resistance.
(a) What is the speed of the shot when Kemal releases it?
(b) How high above the ground does it go? (c) How much time does he have to get out of its way before it returns to the height of the top of his head, $1.83 \mathrm{~m}$ above the ground?

Melissa Walsh
Melissa Walsh
Numerade Educator
09:36

Problem 76

In the first stage of a two-stage rocket, the rocket is fired from the launch pad starting from rest but with a constant acceleration of $3.50 \mathrm{~m} / \mathrm{s}^{2}$ upward. At $25.0 \mathrm{~s}$ after launch, the second stage fires for $10.0 \mathrm{~s}$, which boosts the rocket's velocity to $132.5 \mathrm{~m} / \mathrm{s}$ upward at $35.0 \mathrm{~s}$ after launch. This firing uses up all of the fuel, however, so after the second stage has finished firing, the only force acting on the rocket is gravity. Ignore air resistance.
(a) Find the maximum height that the stage-two rocket reaches above the launch pad. (b) How much time after the end of the stage-two firing will it take for the rocket to fall back to the launch pad? (c) How fast will the stagetwo rocket be moving just as it reaches the launch pad?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
06:03

Problem 77

Two stones are thrown vertically upward from the ground, one with three times the initial speed of the other. (a) If the faster stone takes $10 \mathrm{~s}$ to return to the ground, how long will it take the slower stone to return? (b) If the slower stone reaches a maximum height of $H$, how high (in terms of $H$ ) will the faster stone go? Assume free fall.

Ryan Hood
Ryan Hood
Numerade Educator
05:09

Problem 78

During your summer internship for an aerospace company, you are asked to design a small research rocket. The rocket is to be launched from rest from the earth's surface and is to reach a maximum height of $960 \mathrm{~m}$ above the earth's surface. The rocket's engines give the rocket an upward acceleration of $16.0 \mathrm{~m} / \mathrm{s}^{2}$ during the time $T$ that they fire. After the engines shut off, the rocket is in free fall. Ignore air resistance. What must be the value of $T$ in order for the rocket to reach the required altitude?

Ryan Hood
Ryan Hood
Numerade Educator
08:20

Problem 79

A helicopter carrying Dr. Evil takes off with a constant upward acceleration of $5.0 \mathrm{~m} / \mathrm{s}^{2}$. Secret agent Austin Powers jumps on just as the helicopter lifts off the ground. After the two men struggle for $10.0 \mathrm{~s}$, Powers shuts off the engine and steps out of the helicopter. Assume that the helicopter is in free fall after its engine is shut off, and ignore the effects of air resistance. (a) What is the maximum height above ground reached by the helicopter? (b) Powers deploys a jet pack strapped on his back $7.0 \mathrm{~s}$ after leaving the helicopter, and then he has a constant downward acceleration with magnitude $2.0 \mathrm{~m} / \mathrm{s}^{2} .$ How far is Powers above the ground when the helicopter crashes into the ground?

Zachary Warner
Zachary Warner
Numerade Educator
View

Problem 80

You are climbing in the Altai when you suddenly find yourself at the edge of a fog-shrouded cliff. To find the height of this cliff, you drop a rock from the top; 8.00 s later you hear the sound of the rock hitting the ground at the foot of the cliff.
(a) If you ignore air resistance, how high is the cliff if the speed of sound is $330 \mathrm{~m} / \mathrm{s} ?$
(b) Suppose you had ignored the time it takes the sound to reach you. In that case, would you have overestimated or underestimated the height of the cliff? Explain.

Gregory Devenport
Gregory Devenport
Numerade Educator
06:31

Problem 81

An object is moving along the $x$ -axis. At $t=0$ it has velocity $v_{0 x}=20.0 \mathrm{~m} / \mathrm{s}$. Starting at time $t=0$ it has acceleration $a_{x}=-C t,$ where $C$ has units of $\mathrm{m} / \mathrm{s}^{3} .$ (a) What is the value of $C$ if the object stops in $8.00 \mathrm{~s}$ after $t=0 ?(\mathrm{~b})$ For the value of $\mathrm{C}$ calculated in part (a), how far does the object travel during the $8.00 \mathrm{~s}$ ?

Vishal Gupta
Vishal Gupta
Numerade Educator
03:24

Problem 82

A ball is thrown straight up from the ground with speed $v_{0}$. At the same instant, a second ball is dropped from rest from a height $H$, directly above the point where the first ball was thrown upward. There is no air resistance. (a) Find the time at which the two balls collide.
(b) Find the value of $H$ in terms of $v_{0}$ and $g$ such that at the instant when the balls collide, the first ball is at the highest point of its motion.

Johnny Greavu
Johnny Greavu
University of Minnesota - Twin Cities
07:29

Problem 83

Cars $A$ and $B$ travel in a straight line. The distance of $A$ from the starting point is given as a function of time by $x_{A}(t)=\alpha t+\beta t^{2},$ with $\alpha=2.60 \mathrm{~m} / \mathrm{s}$ and $\beta=1.20 \mathrm{~m} / \mathrm{s}^{2} .$ The distance
of $B$ from the starting point is $x_{B}(t)=\gamma t^{2}-\delta t^{3},$ with $\gamma=2.80 \mathrm{~m} / \mathrm{s}^{2}$ and $\delta=0.20 \mathrm{~m} / \mathrm{s}^{3}$. (a) Which car is ahead just after the two cars leave the starting point?
(b) At what time(s) are the cars at the same point?
(c) At what time(s) is the distance from $A$ to $B$ neither increasing nor decreasing? (d) At what time(s) do $A$ and $B$ have the same acceleration?

Ryan Hood
Ryan Hood
Numerade Educator
01:42

Problem 84

In your physics lab you release a small glider from rest at various points on a long, frictionless air track that is inclined at an angle $\theta$ above the horizontal. With an electronic photocell, you measure the time $t$ it takes the glider to slide a distance $x$ from the release point to the bottom of the track. Your measurements are given in Fig. $\mathbf{P} 2.84,$ which shows a second-order polynomial (quadratic) fit to the plotted data. You are asked to find the glider's acceleration, which is assumed to be constant. There is some error in each measurement, so instead of using a single set of $x$ and $t$ values, you can be more accurate if you use graphical methods and obtain your measured value of the acceleration from the graph. (a) How can you re-graph the data so that the data points fall close to a straight line? (Hint: You might want to plot $x$ or $t,$ or both, raised to some power.) (b) Construct the graph you described in part (a) and find the equation for the straight line that is the best fit to the data points. (c) Use the straight-line fit from part (b) to calculate the acceleration of the glider. (d) The glider is released at a distance $x=1.35 \mathrm{~m}$ from the bottom of the track. Use the acceleration value you obtained in part (c) to calculate the speed of the glider when it reaches the bottom of the track.

Dominador Tan
Dominador Tan
Numerade Educator
04:06

Problem 85

In a physics lab experiment, you release a small steel ball at various heights above the ground and measure the ball's speed just before it strikes the ground. You plot your data on a graph that has the release height (in meters) on the vertical axis and the square of the final speed (in $\mathrm{m}^{2} / \mathrm{s}^{2}$ ) on the horizontal axis. In this graph your data points lie close to a straight line.
(a) Using $g=9.80 \mathrm{~m} / \mathrm{s}^{2}$ and ignoring the effect of air resistance, what is the numerical value of the slope of this straight line? (Include the correct units.) The presence of air resistance reduces the magnitude of the downward acceleration, and the effect of air resistance increases as the speed of the object increases. You repeat the experiment, but this time with a tennis ball as the object being dropped. Air resistance now has a noticeable effect on the data. (b) Is the final speed for a given release height higher than, lower than, or the same as when you ignored air resistance? (c) Is the graph of the release height versus the square of the final speed still a straight line? Sketch the qualitative shape of the graph when air resistance is present.

Ryan Hood
Ryan Hood
Numerade Educator
02:30

Problem 86

A model car starts from rest and travels in a straight line. A smartphone mounted on the car has an app that transmits the magnitude of the car's acceleration (measured by an accelerometer) every second. The results are given in the table:
$$\begin{array}{cc}\text { Time (s) } & \text { Acceleration (m/s }^{2} \text { ) } \\\hline 0 & 5.95 \\1.00 & 5.52 \\2.00 & 5.08 \\3.00 & 4.55 \\4.00 & 3.96 \\5.00 & 3.40\end{array}$$
Each measured value has some experimental error. (a) Plot acceleration versus time and find the equation for the straight line that gives the best fit to the data. (b) Use the equation for $a(t)$ that you found in part (a) to calculate $v(t),$ the speed of the car as a function of time. Sketch the graph of $v$ versus $t$. Is this graph a straight line? (c) Use your result from
(d) Calculate the part
(b) to calculate the speed of the car at $t=5.00 \mathrm{~s}$. distance the car travels between $t=0$ and $t=5.00 \mathrm{~s}$.

Dominador Tan
Dominador Tan
Numerade Educator
05:43

Problem 87

In the vertical jump, an athlete starts from a crouch and jumps upward as high as possible. Even the best athletes spend little more than $1.00 \mathrm{~s}$ in the air (their "hang time"). Treat the athlete as a particle and let $y_{\max }$ be his maximum height above the floor. To explain why he seems to hang in the air, calculate the ratio of the time he is above $y_{\max } / 2$ to the time it takes him to go from the floor to that height. Ignore air resistance.

Ryan Hood
Ryan Hood
Numerade Educator
10:05

Problem 88

A student is running at her top speed of $5.0 \mathrm{~m} / \mathrm{s}$ to catch a bus, which is stopped at the bus stop. When the student is still $40.0 \mathrm{~m}$ from the bus, it starts to pull away, moving with a constant acceleration of $0.170 \mathrm{~m} / \mathrm{s}^{2}$. (a) For how much time and what distance does the student have to run at $5.0 \mathrm{~m} / \mathrm{s}$ before she overtakes the bus? (b) When she reaches the bus, how fast is the bus traveling? (c) Sketch an $x-t$ graph for both the student and the bus. Take $x=0$ at the initial position of the student. (d) The equations you used in part (a) to find the time have a second solution, corresponding to a later time for which the student and bus are again at the same place if they continue their specified motions. Explain the significance of this second solution. How fast is the bus traveling at this point? (e) If the student's top speed is $3.5 \mathrm{~m} / \mathrm{s}$, will she catch the bus? (f) What is the minimum speed the student must have to just catch up with the bus? For what time and what distance does she have to run in that case?

Johnny Greavu
Johnny Greavu
University of Minnesota - Twin Cities
10:47

Problem 89

A ball is thrown straight up from the edge of the roof of a building. A second ball is dropped from the roof $1.00 \mathrm{~s}$ later. Ignore air resistance. (a) If the height of the building is $20.0 \mathrm{~m},$ what must the initial speed of the first ball be if both are to hit the ground at the same time? On the same graph, sketch the positions of both balls as a function of time, measured from when the first ball is thrown. Consider the same situation, but now let the initial speed $v_{0}$ of the first ball be given and treat the height $h$ of the building as an unknown.
(b) What must the height of the building be for both balls to reach the ground at the same time if (i) $v_{0}$ is $6.0 \mathrm{~m} / \mathrm{s}$ and (ii) $v_{0}$ is $9.5 \mathrm{~m} / \mathrm{s} ?$ (c) If $v_{0}$ is greater than some value $v_{\max },$ no value of $h$ exists that allows both balls to hit the ground at the same time. Solve for $v_{\max }$. The value $v_{\max }$ has a simple physical interpretation. What is it? (d) If $v_{0}$ is less than some value $v_{\min }$ no value of $h$ exists that allows both balls to hit the ground at the same time. Solve for $v_{\min }$. The value $v_{\min }$ also has a simple physical interpretation. What is it?

Ryan Hood
Ryan Hood
Numerade Educator
01:03

Problem 90

The human circulatory system is closed - that is, the blood pumped out of the left ventricle of the heart into the arteries is constrained to a series of continuous, branching vessels as it passes through the capillaries and then into the veins as it returns to the heart. The blood in each of the heart's four chambers comes briefly to rest before it is ejected by contraction of the heart muscle.
If the contraction of the left ventricle lasts $250 \mathrm{~ms}$ and the speed of blood flow in the aorta (the large artery leaving the heart) is $0.80 \mathrm{~m} / \mathrm{s}$ at the end of the contraction, what is the average acceleration of a red blood cell as it leaves the heart? (a) $310 \mathrm{~m} / \mathrm{s}^{2} ;(\mathrm{b}) 31 \mathrm{~m} / \mathrm{s}^{2} ;$ (c) $3.2 \mathrm{~m} / \mathrm{s}^{2} ;$ (d) $0.32 \mathrm{~m} / \mathrm{s}^{2}$.

Dominador Tan
Dominador Tan
Numerade Educator
01:12

Problem 91

BIO Blood Flow in the Heart. The human circulatory system is closed - that is, the blood pumped out of the left ventricle of the heart into the arteries is constrained to a series of continuous, branching vessels as it passes through the capillaries and then into the veins as it returns to the heart. The blood in each of the heart's four chambers comes briefly to rest before it is ejected by contraction of the heart muscle.
If the aorta (diameter $d_{\mathrm{a}}$ ) branches into two equal-sized arteries with a combined area equal to that of the aorta, what is the diameter of one of the branches? (a) $\sqrt{d_{a}} ;$ (b) $d_{a} / \sqrt{2} ;$ (c) $2 d_{a} ;$ d) $d_{a} / 2$.

Dominador Tan
Dominador Tan
Numerade Educator
01:01

Problem 92

BIO Blood Flow in the Heart. The human circulatory system is closed - that is, the blood pumped out of the left ventricle of the heart into the arteries is constrained to a series of continuous, branching vessels as it passes through the capillaries and then into the veins as it returns to the heart. The blood in each of the heart's four chambers comes briefly to rest before it is ejected by contraction of the heart muscle. The velocity of blood in the aorta can be measured directly with ultrasound techniques. A typical graph of blood velocity versus time during a single heartbeat is shown in Fig. P2.92. Which statement is the best interpretation of this graph? (a) The blood flow changes direction at about $0.25 \mathrm{~s} ;$ (b) the speed of the blood flow begins to decrease at about $0.10 \mathrm{~s}$;
(c) the acceleration of the blood is greatest in magnitude at about $0.25 \mathrm{~s} ;$
(d) the acceleration of the blood is greatest in magnitude at about $0.10 \mathrm{~s}$.

Dominador Tan
Dominador Tan
Numerade Educator