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College Physics

Raymond A. Serway, Jerry S. Faughn, Chris Vuille

Chapter 2

Motion in One Dimension - all with Video Answers

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Chapter Questions

01:11

Problem 1

The speed of a nerve impulse in the human body is about $100 \mathrm{~m} / \mathrm{s}$. If you accidentally stub your toe in the dark, estimate the time it takes the nerve impulse to travel to your brain.

Massimo Antonelli
Massimo Antonelli
Numerade Educator
02:51

Problem 2

Light travels at a speed of about $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$. How many miles does a pulse of light travel in a time interval of $0.1 \mathrm{~s}$, which is about the blink of an eye? Compare this distance to the diameter of Earth.

Donald Albin
Donald Albin
Numerade Educator
03:02

Problem 3

A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for $30.0 \mathrm{~min}$ at $80.0 \mathrm{~km} / \mathrm{h}, 12.0 \mathrm{~min}$ at $100 \mathrm{~km} / \mathrm{h}$, and
$45.0 \mathrm{~min}$ at $40.0 \mathrm{~km} / \mathrm{h}$ and spends $15.0 \mathrm{~min}$ eating lunch and buying gas. (a) Determine the average speed for the trip. (b) Determine the distance between the initial and final cities along the route.

Averell Hause
Averell Hause
Carnegie Mellon University
04:51

Problem 4

(a) Sand dunes on a desert island move as sand is swept up the windivard side to settle in the leeward side, Such "walking" dunes have been known to travel 20 feet in a year and can travel as much as 100 feet per year in particularly windy times, Calculate the average speed in each case in meters per second. (b) Fingernails grow at the rate of drifting continents, about $10 \mathrm{~mm} / \mathrm{yr}$. Approximately how long did it take for North America to separate from Europe, a distance of about $3000 \mathrm{mi}^{2}$

Donald Albin
Donald Albin
Numerade Educator
02:29

Problem 5

Two boats start together and race across a $60-\mathrm{km}$ -wide lake and back. Boat A goes across at $60 \mathrm{~km} / \mathrm{h}$ and returns at $60 \mathrm{~km} / \mathrm{h}$. Boat $\mathrm{B}$ goes across at $30 \mathrm{~km} / \mathrm{h}$, and its crew, realizing how far behind it is getting, returns at $90 \mathrm{~km} / \mathrm{h}$. Turnaround times are negligible, and the boat that completes the round trip first wins. (a) Which boat wins and by how much? (Or is it a tie?) (b) What is the average velocity of the winning boat?

Averell Hause
Averell Hause
Carnegie Mellon University
03:14

Problem 6

A graph of position versus time for a certain particle moving along the $x$ -axis is shown in Figure $\mathrm{P}_{2} .6$. Find the average velocity in the time intervals from (a) 0 to $2.00 \mathrm{~s}$,
(b) 0 to $4.00 \mathrm{~s}$
(c) $2.00 \mathrm{~s}$ to $4.00 \mathrm{~s}$,
(d) $4.00 \mathrm{~s}$ to $7.00 \mathrm{~s}$, and
(e) 0 to $8.00 \mathrm{~s}$.

Donald Albin
Donald Albin
Numerade Educator
03:37

Problem 7

A motorist drives north for $35.0$ minutes at $85.0 \mathrm{~km} / \mathrm{h}$ and then stops for $15.0$ minutes. He then continues north. traveling $130 \mathrm{~km}$ in $2.00 \mathrm{~h}$. (a) What is his total displacement? (b) What is his average velocity?

Donald Albin
Donald Albin
Numerade Educator
02:26

Problem 8

A tennis player moves in a straight-line path as shown in Figure $\mathrm{P} 2.8$. Find her average velocity in the time intervals from (a) 0 to $1.0 \mathrm{~s}$, (b) 0 to $4.0 \mathrm{~s}$, (c) $1.0 \mathrm{~s}$ to $5.0 \mathrm{~s}$, and
(d) 0 to $\underline{5.0 \mathrm{~s} \text { . }}$

Averell Hause
Averell Hause
Carnegie Mellon University
02:36

Problem 9

Find the instantaneous velocities of the tennis player of Figure $\mathrm{P} 2.8$ at (a) $0.50 \mathrm{~s}$, (b) $2.0 \mathrm{~s}$, (c) $3.0 \mathrm{~s}$, and (d) $4.5 \mathrm{~s}$.

Donald Albin
Donald Albin
Numerade Educator
03:09

Problem 10

Two cars travel in the same direction along a straight highway, one at a constant speed of $55 \mathrm{mi} / \mathrm{h}$ and the other at $70 \mathrm{mi} / \mathrm{h}$. (a) Assuming they start at the same point, how much sooner does the faster car arrive at a destination 10 mi away? (b) How far must the faster car travel before it has a 15 -min lead on the slower car?

Supratim Pal
Supratim Pal
Numerade Educator
03:04

Problem 11

If the average speed of an orbiting space shuttle is $19800 \mathrm{mi} / \mathrm{h}$, determine the time required for it to circle Earth. Make sure you consider that the shuule is orbiting about $2.00 \times 10^{2} \mathrm{mi}$ above Earth's surface and assume that Earth's radius is 3963 miles.

Donald Albin
Donald Albin
Numerade Educator
01:50

Problem 12

An athlete swims the length $L$ of a pool in a time $t_{1}$ and makes the return trip to the starting position in a time $t_{2}$. If she is swimming initially in the positive $x$ direction, determine her average velocities symbolically in (a) the first half of the swim, (b) the second half of the swim, and (c) the round trip. (d) What is her average speed for the round trip?

Efren Serra
Efren Serra
Numerade Educator
05:54

Problem 13

A person takes a trip, driving with a constant speed of $89.5 \mathrm{~km} / \mathrm{h}$, except for a $22.0$ -min rest stop. If the person's average speed is $77.8 \mathrm{~km} / \mathrm{h}$, how much time is spent on the trip and how far does the person travel?

Donald Albin
Donald Albin
Numerade Educator
04:15

Problem 14

A tortoise can run with a speed of $0.10 \mathrm{~m} / \mathrm{s}$, and a hare can run 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for $2.0$ minutes. The tortoise wins by a shell $(20 \mathrm{~cm}) .$ (a) How long does the race take? (b) What is the length of the race?

Averell Hause
Averell Hause
Carnegie Mellon University
07:08

Problem 15

To qualify for the finals in a racing event, a race car must achieve an average speed of $250 \mathrm{~km} / \mathrm{h}$ on a track with a total length of $1600 \mathrm{~m}$. If a particular car covers the first half of the track at an average speed of $230 \mathrm{~km} / \mathrm{h}$, what minimum average speed must it have in the second half of the event in order to qualify?

Donald Albin
Donald Albin
Numerade Educator
14:30

Problem 16

One athlete in a race running on a long, straight track with a constant speed $v_{1}$ is a distance $d$ behind a second athlete running with a constant speed $v_{2} .$ (a) Under what circumstances is the first athlete able to overtake the second athlete? (b) Find the time $t$ it takes the first athlete to overtake the second athlete, in terms of $d, v_{1}$, and $v_{9}$. (c) At what minimum distance $d_{2}$ from the leading athlete must the finish line be located so that the trailing athlete can at least tie for first place? Express $d_{2}$ in terms of $d, v_{1}$, and $v_{2}$ by using the result of part (b).

Donald Albin
Donald Albin
Numerade Educator
02:28

Problem 17

A graph of position versus time for a certain particle moving along the $x$ -axis is shown in Figure $\mathrm{P} 2.6$. Find the instantaneous velocity at the instants (a) $l=1.00 \mathrm{~s}$, (b) $t=3.00 \mathrm{~s},(\mathrm{c}) t=4.50 \mathrm{~s}$, and (d) $t=7.50 \mathrm{~s}$.

Donald Albin
Donald Albin
Numerade Educator
03:39

Problem 18

A race car moves such that its position fits the relationship
$$
x=(5.0 \mathrm{~m} / \mathrm{s}) l+\left(0.75 \mathrm{~m} / \mathrm{s}^{3}\right) t^{3}
$$
where $x$ is measured in meters and $t$ in seconds. (a) Plot a graph of the car's position versus time. (b) Determine the instantaneous velocity of the car at $t=4.0 \mathrm{~s}$, using time intervals of $0.40 \mathrm{~s}, 0.20 \mathrm{~s}$, and $0.10 \mathrm{~s}$. (c) Compare the average velocity during the first $4.0 \mathrm{~s}$ with the results of part (b).

Donald Albin
Donald Albin
Numerade Educator
02:43

Problem 19

Runner A is initially $4.0$ mi west of a flagpole and is running with a constant velocity of $6.0 \mathrm{mi} / \mathrm{h}$ due east. Runner $\mathrm{B}$ is initially $3.0 \mathrm{mi}$ east of the flagpole and is running with a constant velocity of $5.0 \mathrm{mi} / \mathrm{h}$ due west. How far are the runners from the flagpole when they meet?

Averell Hause
Averell Hause
Carnegie Mellon University
05:17

Problem 20

Assume a canister in a straight tube moves with a constant acceleration of $-4.00 \mathrm{~m} / \mathrm{s}^{2}$ and has a velocity of $13.0 \mathrm{~m} / \mathrm{s}$ at $t=0 .$ (a) What is its velocity at $t=1.00 \mathrm{~s} ?$
(b) At $t=2.00 \mathrm{~s}$ ?
(c) At $t=2.50$ s?
(d) At $t=4.00 \mathrm{~s}$ ?
(e) Describe the shape of the canister's velocity versus time graph. (f) What two things must be known at a given time to predict the canister's velocity at any later time?

Donald Albin
Donald Albin
Numerade Educator
12:45

Problem 21

Secretariat ran the Kentucky Derby with times of $25.2 \mathrm{~s}$, $24.0 \mathrm{~s}, 23.8 \mathrm{~s}, 23.2 \mathrm{~s}$, and $23.0 \mathrm{~s}$ for the quarter mile.
(a) Find his average speed during each quarter-mile segment in $\mathrm{ft} / \mathrm{s}$. (b) Assuming that Secretariat's instantaneous speed at the finish line was the same as his average speed during the final quarter mile, find his average acceleration for the entire race in $\mathrm{ft} / \mathrm{s}^{2} .$ (Hint: Recall that horses in the Derby start from rest.)

Donald Albin
Donald Albin
Numerade Educator
01:50

Problem 22

The average person passes out at an acceleration of $7 \mathrm{~g}$ (that is, seven times the gravitational acceleration on Earth). Suppose a car is designed to accelerate at this rate. How much time would be required for the car to accelerate from rest to $60.0$ miles per hour? (The car would need rocket boosters!)

Donald Albin
Donald Albin
Numerade Educator
06:27

Problem 23

A certain car is capable of accelerating at a rate of $10.60 \mathrm{~m} / \mathrm{s}^{2}$. How long does it take for this car to go from a speed of $55 \mathrm{mi} / \mathrm{h}$ to a speed of $60 \mathrm{mi} / \mathrm{h} ?$

Donald Albin
Donald Albin
Numerade Educator
04:01

Problem 24

The velocity vs. time graph for an object moving along a straight path is shown in Figure P2.24. (a) Find the average acceleration of the object during the time intervals 0 to $5.0 \mathrm{~s}, 5.0 \mathrm{~s}$ to $15 \mathrm{~s}$, and 0 to $20 \mathrm{~s}$. (b) Find the instantaneous acceleration at $2.0 \mathrm{~s}, 10 \mathrm{~s}$, and $18 \mathrm{~s}$.

Donald Albin
Donald Albin
Numerade Educator
01:34

Problem 25

A steam catapult launches a jet aircraft from the aircraft carrier John $C$. Stennis, giving it a speed of $175 \mathrm{mi} / \mathrm{h}$ in 2.50 s. (a) Find the average acceleration of the plane.
(b) Assuming the acceleration is constant, find the distance the plane moves.

Averell Hause
Averell Hause
Carnegie Mellon University
01:47

Problem 26

A car is traveling due east at $25.0 \mathrm{~m} / \mathrm{s}$ at some instant.
(a) If its constant acceleration is $0.750 \mathrm{~m} / \mathrm{s}^{2}$ due east, find its velocity after $8.50 \mathrm{~s}$ have elapsed. (b) If its constant acceleration is $0.750 \mathrm{~m} / \mathrm{s}^{2}$ due west, find its velocity after $8.50 \mathrm{~s}$ have elapsed.

Donald Albin
Donald Albin
Numerade Educator
02:13

Problem 27

A car traveling east at $40.0 \mathrm{~m} / \mathrm{s}$ passes a trooper hiding at the roadside. The driver uniformly reduces his speed to $25.0 \mathrm{~m} / \mathrm{s}$ in $3.50 \mathrm{~s}$. (a) What is the magnitude and direction of the car's acceleration as it slows down? (b) How far does the car travel in the $3.5$ -s time period?

Donald Albin
Donald Albin
Numerade Educator
02:31

Problem 28

In 1865 Jules Verne proposed sending men to the Moon by firing a space capsule from a 220 -m-long cannon with final speed of $10.97 \mathrm{~km} / \mathrm{s}$. What would have been the unrealistically large acceleration experienced by the space travelers during their launch? (A human can stand an acceleration of $15 g$ for a short time.) Compare your answer with the free-fall acceleration, $9.80 \mathrm{~m} / \mathrm{s}^{2}$.

Donald Albin
Donald Albin
Numerade Educator
08:15

Problem 29

A truck covers $40.0 \mathrm{~m}$ in $8.50 \mathrm{~s}$ while smoothly slowing down to a final velocity of $2.80 \mathrm{~m} / \mathrm{s}$. (a) Find the truck's original speed. (b) Find its acceleration.

Donald Albin
Donald Albin
Numerade Educator
03:48

Problem 30

A speedboat increases its speed uniformly from $v_{i}=$ $20.0 \mathrm{~m} / \mathrm{s}$ to $v_{f}=30.0 \mathrm{~m} / \mathrm{s}$ in a distance of $2.00 \times 10^{2} \mathrm{~m}$.
(a) Draw a coordinate system for this situation and label the relevant quantities, including vectors. (b) For the given information, what single equation is most appropriate for finding the acceleration? (c) Solve the equation selected in part (b) symbolically for the boat's acceleration in terms of $v_{f}, v_{a}$, and $\Delta x$. (d) Substitute given values, obtaining that acceleration. (e) Find the time it takes the boat to travel the given distance.

Donald Albin
Donald Albin
Numerade Educator
01:45

Problem 31

A Cessna aircraft has a liftoff speed of $120 \mathrm{~km} / \mathrm{h}$.
(a) What minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of $240 \mathrm{~m}$ ? (b) How long does it take the aircraft to become airborne?

Averell Hause
Averell Hause
Carnegie Mellon University
06:40

Problem 32

A truck on a straight road starts from rest and accelerates at $2.0 \mathrm{~m} / \mathrm{s}^{2}$ until it reaches a speed of $20 \mathrm{~m} / \mathrm{s}$. Then the truck travels for $20 \mathrm{~s}$ at constant speed until the brakes are applied, stopping the truck in a uniform manner in an additional $5.0 \mathrm{~s}$. (a) How long is the truck in motion?
(b) What is the average velocity of the truck during the motion described?

Donald Albin
Donald Albin
Numerade Educator
01:19

Problem 33

In a test run, a certain car accelerates uniformly from zero to $24.0 \mathrm{~m} / \mathrm{s}$ in $2.95 \mathrm{~s}$. (a) What is the magnitude of the car's acceleration? (b) How long does it take the car to change its speed from $10.0 \mathrm{~m} / \mathrm{s}$ to $20.0 \mathrm{~m} / \mathrm{s}$ ?
(c) Will doubling the time always double the change in speed? Why?

Anand Jangid
Anand Jangid
Numerade Educator
02:34

Problem 34

A jet plane lands with a speed of $100 \mathrm{~m} / \mathrm{s}$ and can accelerate at a maximum rate of $-5.00 \mathrm{~m} / \mathrm{s}^{2}$ as it comes to rest. (a) From the instant the plane touches the runway, what is the minimum time needed before it can come to rest? (b) Can this plane land on a small tropical island airport where the runway is $0.800 \mathrm{~km}$ long?

Averell Hause
Averell Hause
Carnegie Mellon University
12:03

Problem 35

Speedy Sue, driving at $30.0 \mathrm{~m} / \mathrm{s}$, enters a one-lanc tunnel. She then observes a slow-moving van $155 \mathrm{~m}$ ahead traveling at $5.00 \mathrm{~m} / \mathrm{s}$. Sue applies her brakes but can accelerate only at $-2.00 \mathrm{~m} / \mathrm{s}^{2}$ because the road is wet. Will there be a collision? State how you decide. If yes, determine how far into the tunnel and at what time the collision occurs. If no, determine the distance of closest approach between Sue's car and the van.

Donald Albin
Donald Albin
Numerade Educator
07:16

Problem 36

A record of travel along a straight path is as follows:
1. Start from rest with a constant acceleration of $2.77 \mathrm{~m} / \mathrm{s}^{2}$ for $15.0 \mathrm{~s}$
2. Maintain a constant velocity for the next $2.05 \mathrm{~min}$.
3. Apply a constant negative acceleration of $-9.47 \mathrm{~m} / \mathrm{s}^{2}$ for $4.39 \mathrm{~s}$.
(a) What was the total displacement for the trip? (b) What were the average speeds for legs 1,2, and 3 of the trip, as well as for the complete trip?

Donald Albin
Donald Albin
Numerade Educator
02:46

Problem 37

A train is traveling down a straight track at $20 \mathrm{~m} / \mathrm{s}$ when the engineer applies the brakes, resulting in an acceleration of $-1.0 \mathrm{~m} / \mathrm{s}^{2}$ as long as the train is in motion. How far does the train move during a $40-\mathrm{s}$ time interval starting at the instant the brakes are applied?

Donald Albin
Donald Albin
Numerade Educator
01:46

Problem 38

A car accelerates uniformly from rest to a speed of $40.0 \mathrm{mi} / \mathrm{h}$ in $12.0 \mathrm{~s}$. Find (a) the distance the car travels during this time and (b) the constant acceleration of the ???.

Averell Hause
Averell Hause
Carnegie Mellon University
02:14

Problem 39

|A car starts from rest and travels for $5.0 \mathrm{~s}$ with a uniform acceleration of $+1.5 \mathrm{~m} / \mathrm{s}^{2}$. The driver then applies the brakes, causing a uniform acceleration of $-2.0 \mathrm{~m} / \mathrm{s}^{2} .$ If the brakes are applied for $3.0 \mathrm{~s}$, (a) how fast is the car going at the end of the braking period, and (b) how far has the car gone?

Averell Hause
Averell Hause
Carnegie Mellon University
02:21

Problem 40

A car starts from rest and travels for $t_{1}$ seconds with a uniform acceleration $a_{1} .$ The driver then applies the brakes, causing a uniform acceleration $a_{2} .$ If the brakes are applied for $t_{2}$ seconds, (a) how fast is the car going just before the beginning of the braking period? (b) How far does the car go before the driver begins to brake?
(c) Using the answers to parts (a) and (b) as the initial velocity and position for the motion of the car during braking, what total distance does the car travel? Answers are in terms of the variables $a_{1}, a_{2}, l_{1}$, and $t_{2}$.

Donald Albin
Donald Albin
Numerade Educator
02:57

Problem 41

In the Daytona 500 auto race, a Ford Thunderbird and a Mercedes Benz are moving side by side down a straightaway at $71.5 \mathrm{~m} / \mathrm{s}$. The driver of the Thunderbird realizes that she must make a pit stop, and she smoothly slows to a stop over a distance of $250 \mathrm{~m}$. She spends $5.00 \mathrm{~s}$ in the pit and then accelerates out, reaching her previous speed of $71.5 \mathrm{~m} / \mathrm{s}$ after a distance of $350 \mathrm{~m}$. At this point, how far has the Thunderbird fallen behind the Mercedes Benz. which has continued at a constant speed?

Averell Hause
Averell Hause
Carnegie Mellon University
08:23

Problem 42

A certain cable car in San Francisco can stop in $10 \mathrm{~s}$ when traveling at maximum speed. On one occasion, the driver sees a dog a distance $d \mathrm{~m}$ in front of the car and slams on the brakes instantly. The car reaches the dog $8.0 \mathrm{~s}$ later, and the dog jumps off the track just in time. If the car travels $4.0 \mathrm{~m}$ beyond the position of the dog before $\mathrm{com}-$ ing to a stop, how far was the car from the dog? (Hint:
You will need three equations.

Donald Albin
Donald Albin
Numerade Educator
04:21

Problem 43

A hockey player is standing on his skates on a frozen pond when an opposing player, moving with a uniform speed of $12 \mathrm{~m} / \mathrm{s}$, skates by with the puck. After $3.0 \mathrm{~s}$, the first player makes up his mind to chase his opponent. If he accelerates uniformly at $4.0 \mathrm{~m} / \mathrm{s}^{2}$, (a) how long does it take him to catch his opponent, and (b) how far has he traveled in that time? (Assume the player with the puck remains in motion at constant speed.)

Donald Albin
Donald Albin
Numerade Educator
02:52

Problem 44

A train $400 \mathrm{~m}$ long is moving on a straight track with a speed of $82.4 \mathrm{~km} / \mathrm{h}$. The engineer applies the brakes at a crossing, and later the last car passes the crossing with a speed of $16.4 \mathrm{~km} / \mathrm{h}$. Assuming constant acceleration, determine how long the train blocked the crossing. Disregard the width of the crossing.

Nishant Kumar
Nishant Kumar
Numerade Educator
04:11

Problem 45

A ball is thrown vertically upward with a speed of $25.0 \mathrm{~m} / \mathrm{s}$.
(a) How high does it rise? (b) How long does it take to reach its highest point? (c) How long does the ball take to hit the ground after it reaches its highest point? (d) What is its velocity when it returns to the level from which it started?

Averell Hause
Averell Hause
Carnegie Mellon University
06:16

Problem 46

It is possible to shoot an arrow at a speed as high as $100 \mathrm{~m} / \mathrm{s} .$ (a) If friction is neglected, how high would an arrow launched at this speed rise if shot straight up?
(b) How long would the arrow be in the air?

Jacob Adamczyk
Jacob Adamczyk
Numerade Educator
05:21

Problem 47

A certain freely falling object requires $1.50 \mathrm{~s}$ to travel the last. $30.0 \mathrm{~m}$ before it hits the ground. From what height above the ground did it fall??

Donald Albin
Donald Albin
Numerade Educator
06:02

Problem 48

An attacker at the base of a castle wall $3.65 \mathrm{~m}$ high throws a rock straight up with speed $7.40 \mathrm{~m} / \mathrm{s}$ at a height of $1.55 \mathrm{~m}$ above the ground. (a) Will the rock reach the top of the wall? (b) If so, what is the rock's speed at the top? If not, what initial speed must the rock have to reach the top? (c) Find the change in the speed of a rock thrown straight down from the top of the wall at an initial speed of $7.40 \mathrm{~m} / \mathrm{s}$ and moving between the same two points.
(d) Does the change in speed of the downward-moving rock agree with the magnitude of the speed change of the rock moving upward between the same elevations? Explain physically why or why not.

Narayan Hari
Narayan Hari
Numerade Educator
07:40

Problem 49

Traumatic brain injury such as concussion resul when the head undergoes a very large acceleration. Get erally, an acceleration less than $800 \mathrm{~m} / \mathrm{s}^{2}$ lasting for an length of time will not cause injury, whereas an acceler tion greater than $1000 \mathrm{~m} / \mathrm{s}^{2}$ lasting for at least $1 \mathrm{~ms}$ wi cause injury. Suppose a small child rolls off a bed this $0.40 \mathrm{~m}$ above the floor. If the floor is hardwood, th child's head is brought to rest in approximately $2.0 \mathrm{~mm}$. the floor is carpeted, this stopping distance is increase to about $1.0 \mathrm{~cm}$. Calculate the magnitude and duratio of the deceleration in both cases, to determine the risk injury. Assume the child remains horizontal during th fall to the floor. Note that a more complicated fall coul result in a head velocity greater or less than the speed yo calculate.

Donald Albin
Donald Albin
Numerade Educator
04:39

Problem 50

A small mailbag is released from a helicopter that is descending steadily at $1.50 \mathrm{~m} / \mathrm{s}$. After $2.00 \mathrm{~s}$, (a) what is the speed of the mailbag, and (b) how far is it below the helicopter? (c) What are your answers to parts (a) and (b) if the helicopter is rising steadily at $1.50 \mathrm{~m} / \mathrm{s}$ ?

Averell Hause
Averell Hause
Carnegie Mellon University
03:13

Problem 51

A tennis player tosses a tennis ball straight up and then catches it after $2.00 \mathrm{~s}$ at the same height as the point of release. (a) What is the acceleration of the ball while it is in flight? (b) What is the velocity of the ball when it reaches its maximum height? Find (c) the initial velocity of the ball and (d) the maximum height it reaches.

Averell Hause
Averell Hause
Carnegie Mellon University
04:16

Problem 52

A package is dropped from a helicopter that is descending steadily at a speed $v_{0}$. After $\{$ seconds have elapsed, (a) what is the speed of the package in terms of $v_{0}, g$, and $t ?$ (b) What distance $d$ is it from the helicopter in terms of gand $t$ ? (c) What are the answers to parts (a) and (b) if the helicopter is rising steadily at the same speed?

Donald Albin
Donald Albin
Numerade Educator
11:45

Problem 53

A model rocket is launched straight upward with an initial speed of $50.0 \mathrm{~m} / \mathrm{s} .$ It accelerates with a constant upward acceleration of $2.00 \mathrm{~m} / \mathrm{s}^{2}$ until its engines stop at an altitude of $150 \mathrm{~m}$. (a) What can you say about the motion of the rocket after its engines stop? (b) What is the maximum height reached by the rocket? (c) How long after liftoff does the rocket reach its maximum height? (d) How long is the rocket in the air?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:42

Problem 54

A parachutist with a camera descends in free fall at a speed of $10 \mathrm{~m} / \mathrm{s}$. The parachutist releases the camera at an alutude of $50 \mathrm{~m}$. (a) How long does it take the camera to reach the ground? (b) What is the velocity of the camcra just before it hits the ground?

Donald Albin
Donald Albin
Numerade Educator
04:38

Problem 55

A truck tractor pulls two trailers, one behind the other, at a constant speed of $100 \mathrm{~km} / \mathrm{h}$. It takes $0.600 \mathrm{~s}$ for the big rig to completely pass onto a bridge $400 \mathrm{~m}$ long. For what duration of time is all or part of the truck-trailer combination on the bridge?

Donald Albin
Donald Albin
Numerade Educator
07:00

Problem 56

A speedboat moving at $30.0 \mathrm{~m} / \mathrm{s}$ approaches a no-wake buoy marker $100 \mathrm{~m}$ ahead. The pilot slows the boat with a constant acceleration of $-3.50 \mathrm{~m} / \mathrm{s}^{2}$ by reducing the throttle. (a) How long does it take the boat to reach the buoy? (b) What is the velocity of the boat when it reaches the buoy?

Jacob Adamczyk
Jacob Adamczyk
Numerade Educator
04:56

Problem 57

A bullet is fired through a board $10.0 \mathrm{~cm}$ thick in such a way that the bullet's line of motion is perpendicular to the face of the board. If the initial speed of the bullet is $400 \mathrm{~m} / \mathrm{s}$ and it emerges from the other side of the board with a speed of $300 \mathrm{~m} / \mathrm{s}$, find (a) the acceleration of the bullet as it passes through the board and (b) the total time the bullet is in contact with the board.

Donald Albin
Donald Albin
Numerade Educator
02:28

Problem 58

An indestructible bullet $2.00 \mathrm{~cm}$ long is fired straight through a board that is $10.0 \mathrm{~cm}$ thick. The bullet strikes the board with a speed of $420 \mathrm{~m} / \mathrm{s}$ and emerges with a speed of $280 \mathrm{~m} / \mathrm{s}$. (a) What is the average acceleration of the bullet through the board? (b) What is the total time that the bullet is in contact with the board? (c) What thickness of board (calculated to $0.1 \mathrm{~cm}$ ) would it take to stop the bullet, assuming the acceleration through all boards is the same?

Narayan Hari
Narayan Hari
Numerade Educator
06:18

Problem 59

A student throws a set of keys vertically upward to his fraternity brother, who is in a window $4.00 \mathrm{~m}$ above. The brother's outstretched hand catches the keys $1.50 \mathrm{~s}$ later. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught?

Donald Albin
Donald Albin
Numerade Educator
07:02

Problem 60

A student throws a set of keys vertically upward to his fraternity brother, who is in a window a distance $h$ above. The brother's outstretched hand catches the keys on their way up a time $t$ later. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught? (Answers should be in terms of $h, g$, and $l$.

Donald Albin
Donald Albin
Numerade Educator
03:07

Problem 61

It has been claimed that an insect called the froghopper ( Philaenus spumarius) is the best jumper in the animal kingdom. This insect can accelerate at $4000 \mathrm{~m} / \mathrm{s}^{2}$ over a distance of $2.0 \mathrm{~mm}$ as it straightens its specially designed "jumping legs."
(a) Assuming a uniform acceleration, what is the velocity of the insect after it has accelerated through this short distance, and how long did it take to reach that velocity? (b) How high would the insect jump if air resistance could be ignored? Note that the actual height obtained is about $0.7 \mathrm{~m}$, so air resistance is imporlant here.

Donald Albin
Donald Albin
Numerade Educator
04:43

Problem 62

A ranger in a national park is driving at $35.0 \mathrm{mi} / \mathrm{h}$ when a deer jumps into the road $200 \mathrm{ft}$ ahead of the vehicle. After a reaction time $t$, the ranger applies the brakes to produce an acceleration $a=-9.00 \mathrm{ft} / \mathrm{s}^{2} .$ What is the maximum reaction time allowed if she is to avoid hitting the
deer?

Donald Albin
Donald Albin
Numerade Educator
02:29

Problem 63

A ball is thrown upward from the ground with an initial speed of $25 \mathrm{~m} / \mathrm{s} ;$ at the same instant, another ball is dropped from a building $15 \mathrm{~m}$ high. After how long will the balls be at the same height?

Donald Albin
Donald Albin
Numerade Educator
05:04

Problem 64

To pass a physical education class at a university, a student must run $1.0 \mathrm{mi}$ in $12 \mathrm{~min}$. After running for $10 \mathrm{~min}$, she still has $500 \mathrm{yd}$ to go. If her maximum acceleration is $0.15 \mathrm{~m} / \mathrm{s}^{2}$, can she make it? If the answer is no, determine what acceleration she would need to be successful.

Donald Albin
Donald Albin
Numerade Educator
06:17

Problem 65

Two students are on a balcony $19.6 \mathrm{~m}$ above the street. One student throws a ball vertically downward at $14.7 \mathrm{~m} / \mathrm{s} ;$ at the same instant, the other student throws a ball vertically upward at the same speed. The second ball just misses the balcony on the way down. (a) What is the difference in the two balls' time in the air? (b) What is the velocity of each ball as it strikes the ground? (c) How far apart are the balls $0.800 \mathrm{~s}$ after they are thrown?

Donald Albin
Donald Albin
Numerade Educator
11:03

Problem 66

Two students are on a balcony a distance $h$ above the street. One student throws a ball vertically downward at a speed $v_{0}$; at the same time, the other student throws a ball vertically upward at the same speed. Answer the following symbolically in terms of $v_{0}, g, h$, and $t$. (a) Write the kinematic equation for the $y$ -coordinate of each ball. (b) Set the equations found in part (a) equal to height 0 and solve each for $t$ symbolically using the quadratic formula. What is the difference in the two balls' time in the air? (c) Use the time-independent kinematics equation to find the velocity of each ball as it strikes the ground.
(d) How far apart are the balls at a time $t$ after they are released and before they strike the ground?

Donald Albin
Donald Albin
Numerade Educator
11:29

Problem 67

You drop a ball from a window on an upper floor of a building and it is caught by a friend on the ground when the ball is moving with speed $v_{f}$. You now repeat the drop, but you have a friend on the street below throw another ball upward at speed $v_{f}$ exactly at the same time that you drop your ball from the window. The two balls are initially separated by $28.7 \mathrm{~m} .$ (a) At what time do they pass each other? (b) At what location do they pass each other relative the window?

Donald Albin
Donald Albin
Numerade Educator
04:18

Problem 68

The driver of a truck slams on the brakes when he sees a tree blocking the road. The truck slows down uniformly with an acceleration of $-5.60 \mathrm{~m} / \mathrm{s}^{2}$ for $4.20 \mathrm{~s}$, making skid marks $62.4 \mathrm{~m}$ long that end at the tree. With what speed does the truck then strike the tree?

Donald Albin
Donald Albin
Numerade Educator
02:11

Problem 69

Emily challenges her husband, David, to catch a $\$ 1$ bill as follows. She holds the bill vertically as in Figure $\mathrm{P} 2.69$, with the center of the bill between David's index finger and thumb. David must catch the bill after Emily releases it without moving his hand downward. If his reaction time is $0.2 \mathrm{~s}$, will he succeed? Explain your reasoning. (This challenge is a good trick you might want to try with your friends.)

Donald Albin
Donald Albin
Numerade Educator
06:48

Problem 70

A mountain climber stands at the top of a $50.0-\mathrm{m}$ cliff that overhangs a calm pool of water. She throws two stones vertically downward $1.00 \mathrm{~s}$ apart and observes that they cause a single splash. The first stone had an initial velocity of $-2.00 \mathrm{~m} / \mathrm{s}$. (a) How long after release of the first stone did the two stones hit the water? (b) What initial velocity must the second stone have had, given that they hit the water simultaneously? (c) What was the velocity of each stone at the instant it hit the water?

Donald Albin
Donald Albin
Numerade Educator
09:30

Problem 71

An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at $+40 \mathrm{ft} / \mathrm{s}^{2} .$ After some time $t_{1}$, the rocket engine is shut down and the sled moves with constant velocity $v$ for a time $l_{2} .$ If the total distance traveled by the sled is $17500 \mathrm{ft}$ and the total time is $90 \mathrm{~s}$, find (a) the times $t_{1}$ and $t_{2}$ and (b) the velocity $v$ At the 17500 -ft mark, the sled begins to accelerate at $-20 \mathrm{ft} / \mathrm{s}^{2},(\mathrm{c})$ What is the final position of the sled when it comes to rest? (d) How long does it take to come to rest?

Donald Albin
Donald Albin
Numerade Educator
05:49

Problem 72

In Bosnia, the ultimate test of a young man's courage used to be to jump off a 400 -year-old bridge (now destroyed) into the River Neretva, $23 \mathrm{~m}$ below the bridge. (a) How long did the jump last? (b) How fast was the jumper trayeling upon impact with the river? (c) If the speed of sound in air is $340 \mathrm{~m} / \mathrm{s}$, how long after the jumper took off did a spectator on the bridge hear the splash?

Donald Albin
Donald Albin
Numerade Educator
02:39

Problem 73

A person sees a lightning bolt pass close to an airplane that is flying in the distance. The person hears thunder $5.0 \mathrm{~s}$ after seeing the bolt and sees the airplane overhead $10 \mathrm{~s}$ after hearing the thunder. The speed of sound in air is $1100 \mathrm{ft} / \mathrm{s}$. (a) Find the distance of the airplane from the person at the instant of the bolt. (Neglect the time it takes the light to travel from the bolt to the eye.)
(b) Assuming the plane travels with a constant speed toward the person, find the velocity of the airplane.
(c) Look up the speed of light in air and defend the approximation used in part (a).

Donald Albin
Donald Albin
Numerade Educator
03:18

Problem 74

A glider on an air track carries a flag of length $\bar{\ell}$ through a stationary photogate, which measures the time interval $\Delta l_{d}$ during which the flag blocks a beam of infrared light passing across the photogate. The ratio $v_{d}=$ $\ell / \Delta t_{d}$ is the average velocity of the glider over this part of its motion. Suppose the glider moves with constant accelcration. (a) Is $v_{d}$ necessarily equal to the instantaneous velocity of the glider when it is halfway through the photogate in space? Explain. (b) Is $v_{d}$ equal to the instantaneous velocity of the glider when it is halfway through the photogate in time? Explain.

Donald Albin
Donald Albin
Numerade Educator
03:21

Problem 75

A stuntman sitting on a tree limb wishes to drop vertically onto a horse galloping under the tree. The constant speed of the horse is $10.0 \mathrm{~m} / \mathrm{s}$, and the man is initially $3.00 \mathrm{~m}$ above the level of the saddle. (a) What must be the horizontal distance between the saddle and the limb when the man makes his move? (b) How long is he in the air?

Averell Hause
Averell Hause
Carnegie Mellon University