College Physics: A Strategic Approach Volume 1

Randall D. Knight, Brian Jones, Stuart Field

Chapter 2

Motion in One Dimension - all with Video Answers

Educators

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Chapter Questions

Problem 1

Figure $\mathrm{P} 2.1$ shows a motion diagram of a car traveling down a street. The camera took one frame every second. A distance scale is provided.
a. Measure the $x$ -value of the car at each dot. Place your data in a table, similar to Table 2.1 , showing each position and the instant of time at which it occurred.
b. Make a graph of $x$ versus $t,$ using the data in your table. Because you have data only at certain instants of time, your graph should consist of dots that are not connected together.

Hubert Agamasu

Hubert Agamasu

Numerade Educator

Problem 2

For each motion diagram in Figure $\mathrm{P} 2.2$, determine the sign (positive or negative) of the position and the velocity.

Vishal Gupta

Numerade Educator

Problem 3

Write a short description of the motion of a real object for which Figure $\mathrm{P} 2.3$ would be a realistic position-versus-time graph.

Hubert Agamasu

Numerade Educator

Problem 4

Write a short description of the motion of a real object for which Figure $\mathrm{P} 2.4$ would be a realistic position-versus-time graph.

Hubert Agamasu

Numerade Educator

Problem 5

The position graph of Figure $\mathrm{P} 2.5$ shows a dog slowly sneaking up on a squirrel, then putting on a burst of speed.
a. For how many seconds does the dog move at the slower speed?
b. Draw the dog's velocity-versus-time graph. Include a numerical scale on both axes.

Massimo Antonelli

Massimo Antonelli

Numerade Educator

Problem 6

The position graph of Figure $\mathrm{P} 2.6$ represents the motion of a ball being rolled back and forth by two children.
a. At what positions are the two children sitting?
b. Draw the ball's velocity-versus-time graph. Include a numerical scale on both axes.

Hubert Agamasu

Numerade Educator

Problem 7

A rural mail carrier is driving slowly, putting mail in mailboxes near the road. He overshoots one mailbox, stops, shifts into reverse, and then backs up until he is at the right spot. The velocity graph of Figure $\mathrm{P} 2.7$ represents his motion.
a. Draw the mail carrier's position-versus-time graph. Assume that $x=0 \mathrm{~m}$ at $t=0 \mathrm{~s}$
b. What is the position of the mailbox?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 8

For the velocity-versus-time graph of Figure $\mathrm{P} 2.8$ :
a. Draw the corresponding position-versus-time graph. Assume that $x=0 \mathrm{~m}$ at $t=0 \mathrm{~s}$
b. What is the object's position at $t=12 \mathrm{~s} ?$
c. Describe a moving object that could have these graphs.

Hubert Agamasu

Numerade Educator

Problem 9

A bicyclist has the position-versus-time graph shown in Figure $\mathrm{P} 2.9 .$ What is the bicyclist's velocity at $t=10 \mathrm{~s},$ at $t=25 \mathrm{~s},$ and at $t=35 \mathrm{~s} ?$

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 10

In college softball, the distance from the pitcher's mound to the batter is 43 feet. If the ball leaves the bat at $100 \mathrm{mph}$, how much time elapses between the hit and the ball reaching the pitcher?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 11

Alan leaves Los Angeles at 8: 00 A.M. to drive to San Francisco, 400 mi away. He travels at a steady 50 mph. Beth leaves Los Angeles at 9: 00 A.M. and drives a steady 60 mph.
a. Who gets to San Francisco first?
b. How long does the first to arrive have to wait for the sec-

Vishal Gupta

Numerade Educator

Problem 12

Richard is driving home to visit his parents. $125 \mathrm{mi}$ of the trip are on the interstate highway where the speed limit is $65 \mathrm{mph}$. Normally Richard drives at the speed limit, but today he is running late and decides to take his chances by driving at 70 mph. How many minutes does he save?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 13

In a $5.00 \mathrm{~km}$ race, one runner runs at a steady $12.0 \mathrm{~km} / \mathrm{h}$ and another runs at $14.5 \mathrm{~km} / \mathrm{h}$. How long does the faster runner have to wait at the finish line to see the slower runner cross?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 14

In an $8.00 \mathrm{~km}$ race, one runner runs at a steady $11.0 \mathrm{~km} / \mathrm{h}$ and another runs at $14.0 \mathrm{~km} / \mathrm{h}$. How far from the finish line is the slower runner when the faster runner finishes the race?

00000 00000

Numerade Educator

Problem 15

A car moves with constant velocity along a straight road. Its position is $x_{1}=0 \mathrm{~m}$ at $t_{1}=0 \mathrm{~s}$ and is $x_{2}=30 \mathrm{~m}$ at $t_{2}=3.0 \mathrm{~s}$
Answer the following by considering ratios, without computing the car's velocity.
a. What is the car's position at $t=1.5 \mathrm{~s} ?$
b. What will be its position at $t=9.0 \mathrm{~s} ?$

00000 00000

Numerade Educator

Problem 16

While running a marathon, a long-distance runner uses a stopwatch to time herself over a distance of $100 \mathrm{~m}$. She finds that she runs this distance in $18 \mathrm{~s}$. Answer the following by considering ratios, without computing her velocity.
a. If she maintains her speed, how much time will it take her to run the next $400 \mathrm{~m}$ ?
b. How long will it take her to run a mile at this speed?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 17

Figure $\mathrm{P} 2.17$ shows the position graph of a particle.
a. Draw the particle's velocity graph for the interval $0 \mathrm{~s} \leq t \leq 4 \mathrm{~s}$
b. Does this particle have a turning point or points? If so, at what time or times?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 18

A somewhat idealized graph of the speed of the blood in the ascending aorta during one beat of the heart appears as in Figure $\mathrm{P} 2.18$
a. Approximately how far, in $\mathrm{cm},$ does the blood move during one beat?
b. Assume similar data for the motion of the blood in your aorta. Estimate how many beats of the heart it will it take the blood to get from your heart to your brain.

Hubert Agamasu

Numerade Educator

Problem 19

A car starts from $x_{\mathrm{i}}=10 \mathrm{~m}$ at $t_{\mathrm{i}}=0 \mathrm{~s}$ and moves with the velocity graph shown in Figure $\mathrm{P} 2.19 .$
a. What is the object's position at $t=2 \mathrm{~s}, 3 \mathrm{~s}$ and $4 \mathrm{~s} ?$
b. Does this car ever change direction? If so, at what time?

Vishal Gupta

Numerade Educator

Problem 20

Figure $\mathrm{P} 2.20$ shows a graph of actual position-versus-time data for a particular type of drag racer known as a "funny car."
a. Estimate the car's velocity at $2.0 \mathrm{~s}$.
b. Estimate the car's velocity at $4.0 \mathrm{~s}$.

Hubert Agamasu

Numerade Educator

Problem 21

Figure $\mathrm{P} 2.21$ shows the velocity graph of a bicycle. Draw the bicycle's acceleration graph for the interval $0 \mathrm{~s} \leq t \leq 4 \mathrm{~s}$ Give both axes an appropriate numerical scale.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 22

Figure $\mathrm{P} 2.22$ shows the velocity graph of a train that starts from the origin at $t=0 \mathrm{~s}$
a. Draw position and acceleration graphs for the train.
b. Find the acceleration of the train at $t=3.0 \mathrm{~s}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 23

For each motion diagram shown earlier in Figure $\mathrm{P} 2.2,$ determine the sign (positive or negative) of the acceleration.

00000 00000

Numerade Educator

Problem 24

Figure $\mathrm{P} 2.18$ showed data for the speed of blood in the aorta. Determine the magnitude of the acceleration for both phases, speeding up and slowing down.

Vishal Gupta

Numerade Educator

Problem 25

Figure $\mathrm{P} 2.25$ is a somewhat simplified velocity graph for Olympic sprinter Carl Lewis starting a $100 \mathrm{~m}$ dash. Estimate his acceleration during each of the intervals $\mathrm{A}, \mathrm{B},$ and $\mathrm{C}$.

Prashant Bana

Numerade Educator

Problem 26

A Thomson's gazelle can reach a speed of $13 \mathrm{~m} / \mathrm{s}$ in $3.0 \mathrm{~s}$. A lion can reach a speed of $9.5 \mathrm{~m} / \mathrm{s}$ in $1.0 \mathrm{~s}$. A trout can reach a speed of $2.8 \mathrm{~m} / \mathrm{s}$ in $0.12 \mathrm{~s}$. Which animal has the largest acceleration?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 27

When striking, the pike, a predatory fish, can accelerate from rest to a speed of $4.0 \mathrm{~m} / \mathrm{s}$ in $0.11 \mathrm{~s}$
a. What is the acceleration of the pike during this strike?
b. How far does the pike move during this strike?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 28

a. What constant acceleration, in SI units, must a car have to go from zero to 60 mph in 10 s?
b. What fraction of $g$ is this?
c. How far has the car traveled when it reaches 60 mph? Give your answer both in SI units and in feet.

Justin Swantek

Numerade Educator

Problem 29

Light-rail passenger trains that provide transportation within and between cities are capable of modest accelerations. The magnitude of the maximum acceleration is typically $1.3 \mathrm{~m} / \mathrm{s}^{2}$, but the driver will usually maintain a constant acceleration that is less than the maximum. A train travels through a congested part of town at $5.0 \mathrm{~m} / \mathrm{s}$. Once free of this area, it speeds up to 12 $\mathrm{m} / \mathrm{s}$ in $8.0 \mathrm{~s}$. At the edge of town, the driver again accelerates, with the same acceleration, for another $16 \mathrm{~s}$ to reach a higher cruising speed. What is the final speed?

Vishal Gupta

Numerade Educator

Problem 30

A speed skater moving across frictionless ice at $8.0 \mathrm{~m} / \mathrm{s}$ hits a $5.0-\mathrm{m}$ -wide patch of rough ice. She slows steadily, then continues on at $6.0 \mathrm{~m} / \mathrm{s}$. What is her acceleration on the rough ice?

Mayukh Banik

Numerade Educator

Problem 31

A small propeller airplane can comfortably achieve a high enough speed to take off on a runway that is $1 / 4$ mile long. A large, fully loaded passenger jet has about the same acceleration from rest, but it needs to achieve twice the speed to take off. What is the minimum runway length that will serve? Hint: You can solve this problem using ratios without having any additional information.

Prabhat Tyagi

Numerade Educator

Problem 32

Figure $\mathrm{P} 2.32$ shows a velocity-versus-time graph for a particle moving along the $x$ -axis. At $t=0 \mathrm{~s},$ assume that $x=0 \mathrm{~m}$
a. What are the particle's position, velocity, and acceleration at $t=1.0 \mathrm{~s} ?$
b. What are the particle's position, velocity, and acceleration at $t=3.0 \mathrm{~s} ?$

Vishal Gupta

Numerade Educator

Problem 33

A driver has a reaction time of $0.50 \mathrm{~s},$ and the maximum deceleration of her car is $6.0 \mathrm{~m} / \mathrm{s}^{2}$. She is driving at $20 \mathrm{~m} / \mathrm{s}$ when suddenly she sees an obstacle in the road $50 \mathrm{~m}$ in front of her. Can she stop the car in time to avoid a collision?

Mayukh Banik

Numerade Educator

Problem 34

Chameleons catch insects with their tongues, which they can rapidly extend to great lengths. In a typical strike, the chameleon's tongue accelerates at a remarkable $250 \mathrm{~m} / \mathrm{s}^{2}$ for $20 \mathrm{~ms},$ then travels at constant speed for another $30 \mathrm{~ms}$. During this total time of $50 \mathrm{~ms}, 1 / 20$ of a second, how far does the tongue reach?

00000 00000

Numerade Educator

Problem 35

You're driving down the highway late one night at $20 \mathrm{~m} / \mathrm{s}$ when a deer steps onto the road $35 \mathrm{~m}$ in front of you. Your reaction time before stepping on the brakes is $0.50 \mathrm{~s},$ and the maximum deceleration of your car is $10 \mathrm{~m} / \mathrm{s}^{2}$.
a. How much distance is between you and the deer when you come to a stop?
b. What is the maximum speed you could have and still not hit the deer?

Mayukh Banik

Numerade Educator

Problem 36

A light-rail train going from one station to the next on a straight section of track accelerates from rest at $1.1 \mathrm{~m} / \mathrm{s}^{2}$ for $20 \mathrm{~s}$. It then proceeds at constant speed for $1100 \mathrm{~m}$ before slowing down at $2.2 \mathrm{~m} / \mathrm{s}^{2}$ until it stops at the station.
a. What is the distance between the stations?
b. How much time does it take the train to go between the stations?

00000 00000

Numerade Educator

Problem 37

A simple model for a person running the $100 \mathrm{~m}$ dash is to assume the sprinter runs with constant acceleration until reaching top speed, then maintains that speed through the finish line. If a sprinter reaches his top speed of $11.2 \mathrm{~m} / \mathrm{s}$ in $2.14 \mathrm{~s}$, what will be his total time?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 38

Ball bearings can be made by letting spherical drops of molten metal fall inside a tall tower - called a shot tower-and solidify as they fall.
a. If a bearing needs 4.0 s to solidify enough for impact, how high must the tower be?
b. What is the bearing's impact velocity?

Mayukh Banik

Numerade Educator

Problem 39

In the chapter, we saw that a person's reaction time is generally not quick enough to allow the person to catch a dollar bill dropped between the fingers. If a typical reaction time in this case is $0.25 \mathrm{~s}$, how long would a bill need to be for a person to have a good chance of catching it?

Hubert Agamasu

Numerade Educator

Problem 40

A ball is thrown vertically upward with a speed of $19.6 \mathrm{~m} / \mathrm{s}$.
a. What are the ball's velocity and height after 1.00,2.00,3.00 , and $4.00 \mathrm{~s} ?$
b. Draw the ball's velocity-versus-time graph. Give both axes an appropriate numerical scale.

Vishal Gupta

Numerade Educator

Problem 41

A student at the top of a building of height $h$ throws ball $\mathrm{A}$ straight upward with speed $v_{0}$ and throws ball B straight downward with the same initial speed.
a. Compare the balls' accelerations, both direction and magnitude, immediately after they leave her hand. Is one acceleration larger than the other? Or are the magnitudes equal?
b. Compare the final speeds of the balls as they reach the ground. Is one larger than the other? Or are they equal?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 42

Excellent human jumpers can leap straight up to a height of $110 \mathrm{~cm}$ off the ground. To reach this height, with what speed would a person need to leave the ground?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 43

A football is kicked straight up into the air; it hits the ground $5.2 \mathrm{~s}$ later.
a. What was the greatest height reached by the ball? Assume it is kicked from ground level.
b. With what speed did it leave the kicker's foot?

Massimo Antonelli

Massimo Antonelli

Numerade Educator

Problem 44

In an action movie, the villain is rescued from the ocean by grabbing onto the ladder hanging from a helicopter. He is so intent on gripping the ladder that he lets go of his briefcase of counterfeit money when he is $130 \mathrm{~m}$ above the water. If the briefcase hits the water 6.0 s later, what was the speed at which the helicopter was ascending?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 45

A rock climber stands on top of a $50-\mathrm{m}$ -high cliff overhanging a pool of water. He throws two stones vertically downward $1.0 \mathrm{~s}$ apart and observes that they cause a single splash. The initial speed of the first stone was $2.0 \mathrm{~m} / \mathrm{s}$.
a. How long after the release of the first stone does the second stone hit the water?
b. What was the initial speed of the second stone?
c. What is the speed of each stone as they hit the water?

Vishal Gupta

Numerade Educator

Problem 46

Actual velocity data for a lion pursuing prey are shown in Figure P2.46. Estimate:
a. The initial acceleration of the lion.
b. The acceleration of the lion at $2 \mathrm{~s}$ and at $4 \mathrm{~s}$.
c. The distance traveled by the lion between $0 \mathrm{~s}$ and $8 \mathrm{~s}$.

00000 00000

Numerade Educator

Problem 47

Concern nerve impulses, electrical signals propagated along nerve fibers consisting of many axons (fiberlike extensions of nerve cells) connected end-to-end. Axons come in two varieties: insulated axons with a sheath made of myelin, and uninsulated axons with no such sheath. Myelinated (sheathed) axons conduct nerve impulses much faster than unmyelinated (unsheathed) axons. The impulse speed depends on the diameter of the axons and the sheath, but a typical myelinated axon transmits nerve impulses at a speed of about $25 \mathrm{~m} / \mathrm{s}$ much faster than the typical $2.0 \mathrm{~m} / \mathrm{s}$ for an unmyelinated axon. Figure P2.47 shows small portions of three nerve fibers consisting of axons of equal size. Two-thirds of the axons in fiber $\mathrm{B}$ are myelinated.
Suppose nerve impulses simultaneously enter the left side of the nerve fibers sketched in Figure $\mathrm{P} 2.47,$ then propagate to the right. Draw qualitatively accurate position and velocity graphs for the nerve impulses in all three cases. A nerve fiber is made up of many axons, but show the propagation of the impulses only over the six axons shown here.

AH

Alexander Hrin

Numerade Educator

Problem 48

Concern nerve impulses, electrical signals propagated along nerve fibers consisting of many axons (fiberlike extensions of nerve cells) connected end-to-end. Axons come in two varieties: insulated axons with a sheath made of myelin, and uninsulated axons with no such sheath. Myelinated (sheathed) axons conduct nerve impulses much faster than unmyelinated (unsheathed) axons. The impulse speed depends on the diameter of the axons and the sheath, but a typical myelinated axon transmits nerve impulses at a speed of about $25 \mathrm{~m} / \mathrm{s}$ much faster than the typical $2.0 \mathrm{~m} / \mathrm{s}$ for an unmyelinated axon. Figure P2.47 shows small portions of three nerve fibers consisting of axons of equal size. Two-thirds of the axons in fiber $\mathrm{B}$ are myelinated.
Suppose that the nerve fibers in Figure $\mathrm{P} 2.47$ connect a finger to your brain, a distance of $1.2 \mathrm{~m}$.
a. What are the travel times of a nerve impulse from finger to brain along fibers $A$ and $C ?$
b. For fiber $\mathrm{B}, 2 / 3$ of the length is composed of myelinated axons, $1 / 3$ unmyelinated axons. Compute the travel time for a nerve impulse on this fiber.
c. When you touch a hot stove with your finger, the sensation of pain must reach your brain as a nerve signal along a nerve fiber before your muscles can react. Which of the three fibers gives you the best protection against a burn? Are any of these fibers unsuitable for transmitting urgent sensory information?

AH

Alexander Hrin

Numerade Educator

Problem 49

A truck driver has a shipment of apples to deliver to a destination 440 miles away. The trip usually takes him 8 hours. Today he finds himself daydreaming and realizes 120 miles into his trip that he is running 15 minutes later than his usual pace at this point. At what speed must he drive for the remainder of the trip to complete the trip in the usual amount of time?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 50

When you sneeze, the air in your lungs accelerates from rest to approximately $150 \mathrm{~km} / \mathrm{h}$ in about 0.50 seconds.
a. What is the acceleration of the air in $\mathrm{m} / \mathrm{s}^{2}$ ?
b. What is this acceleration, in units of $g$ ?

00000 00000

Numerade Educator

Problem 51

Figure $\mathrm{P} 2.51$ shows the motion diagram, made at two frames of film per second, of a ball rolling along a track. The track has a 3.0 -m-long sticky section.
a. Use the scale to determine the positions of the center of the ball. Place your data in a table, similar to Table 2.1 , showing each position and the instant of time at which it occurred.
b. Make a graph of $x$ versus $t$ for the ball. Because you have data only at certain instants of time, your graph should consist of dots that are not connected together.
c. What is the change in the ball's position from $t=0 \mathrm{~s}$ to $t=1.0 \mathrm{~s} ?$
d. What is the change in the ball's position from $t=2.0 \mathrm{~s}$ to $t=4.0 \mathrm{~s} ?$
e. What is the ball's velocity before reaching the sticky section?
f. What is the ball's velocity after passing the sticky section?
g. Determine the ball's acceleration on the sticky section of the track.

00000 00000

Numerade Educator

Problem 52

Julie drives 100 mi to Grandmother's house. On the way to Grandmother's, Julie drives half the distance at $40 \mathrm{mph}$ and half the distance at $60 \mathrm{mph}$. On her return trip, she drives half the time at 40 mph and half the time at 60 mph.
a. How long does it take Julie to complete the trip to Grandmother's house?
b. How long does the return trip take?

00000 00000

Numerade Educator

Problem 53

The takeoff speed for an Airbus A320 jetliner is $80 \mathrm{~m} / \mathrm{s}$. Velocity data measured during takeoff are as shown in the table.
a. What is the takeoff speed in miles per hour?
b. What is the jetliner's acceleration during takeoff?
c. At what time do the wheels leave the ground?
d. For safety reasons, in case of an aborted takeoff, the runway must be three times the takeoff distance. Can an A320 take off safely on a 2.5 -mi-long runway?

Vishal Gupta

Numerade Educator

Problem 54

Does a real automobile have constant acceleration? Measured data for a Porsche 944 Turbo at maximum acceleration are as shown in the table.
a. Convert the velocities to $\mathrm{m} / \mathrm{s}$, then make a graph of velocity versus time. Based on your graph, is the acceleration constant? Explain.
b. Draw a smooth curve through the points on your graph, then use your graph to estimate the car's acceleration at $2.0 \mathrm{~s}$ and 8.0 s. Give your answer in SI units. Hint: Remember that acceleration is the slope of the velocity graph.

00000 00000

Numerade Educator

Problem 55

People hoping to travel to other worlds are faced with huge challenges. One of the biggest is the time required for a journey. The nearest star is $4.1 \times 10^{16} \mathrm{~m}$ away. Suppose you had a spacecraft that could accelerate at $1.0 g$ for half a year, then continue at a constant speed. (This is far beyond what can be achieved with any known technology.) How long would it take you to reach the nearest star to earth?

Gayathri Janakiraman Paramasivan

Gayathri Janakiraman Paramasivan

Numerade Educator

Problem 56

You are driving to the grocery store at $20 \mathrm{~m} / \mathrm{s}$. You are $110 \mathrm{~m}$ from an intersection when the traffic light turns red. Assume that your reaction time is $0.70 \mathrm{~s}$ and that your car brakes with constant acceleration.
a. How far are you from the intersection when you begin to apply the brakes?
b. What acceleration will bring you to rest right at the intersection?
c. How long does it take you to stop?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 57

When you blink your eye, the upper lid goes from rest with your eye open to completely covering your eye in a time of $0.024 \mathrm{~s}$.
a. Estimate the distance that the top lid of your eye moves during a blink.
b. What is the acceleration of your eyelid? Assume it to be constant.
c. What is your upper eyelid's final speed as it hits the bottom eyelid?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 58

A bush baby, an African primate, is capable of leaping vertically to the remarkable height of $2.3 \mathrm{~m}$. To jump this high, the bush baby accelerates over a distance of $0.16 \mathrm{~m}$ while rapidly extending its legs. The acceleration during the jump is approximately constant. What is the acceleration in $\mathrm{m} / \mathrm{s}^{2}$ and in $g$ 's?

Hubert Agamasu

Numerade Educator

Problem 59

When jumping, a flea reaches a takeoff speed of $1.0 \mathrm{~m} / \mathrm{s}$ over a distance of $0.50 \mathrm{~mm}$.
a. What is the flea's acceleration during the jump phase?
b. How long does the acceleration phase last?
c. If the flea jumps straight up, how high will it go? (Ignore air resistance for this problem; in reality, air resistance plays a large role, and the flea will not reach this height.)

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 60

Certain insects can achieve seemingly impossible accelerations while jumping. The click beetle accelerates at an astonishing $400 g$ over a distance of $0.60 \mathrm{~cm}$ as it rapidly bends its thorax, making the "click" that gives it its name.
a. Assuming the beetle jumps straight up, at what speed does it leave the ground?
b. How much time is required for the beetle to reach this speed?
c. Ignoring air resistance, how high would it go?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 61

Divers compete by diving into a 3.0 -m-deep pool from a platform $10 \mathrm{~m}$ above the water. What is the magnitude of the minimum acceleration in the water needed to keep a diver from hitting the bottom of the pool? Assume the acceleration is constant.

Hubert Agamasu

Numerade Educator

Problem 62

A student standing on the ground throws a ball straight up. The ball leaves the student's hand with a speed of $15 \mathrm{~m} / \mathrm{s}$ when the hand is $2.0 \mathrm{~m}$ above the ground. How long is the ball in the air before it hits the ground? (The student moves her hand out of the way.)

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 63

A rock is tossed straight up with a speed of $20 \mathrm{~m} / \mathrm{s}$. When it returns, it falls into a hole $10 \mathrm{~m}$ deep.
a. What is the rock's velocity as it hits the bottom of the hole?
b. How long is the rock in the air, from the instant it is released until it hits the bottom of the hole?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 64

A $200 \mathrm{~kg}$ weather rocket is loaded with $100 \mathrm{~kg}$ of fuel and fired straight up. It accelerates upward at $30.0 \mathrm{~m} / \mathrm{s}^{2}$ for $30.0 \mathrm{~s}$ then runs out of fuel. Ignore any air resistance effects.
a. What is the rocket's maximum altitude?
b. How long is the rocket in the air?
c. Draw a velocity-versus-time graph for the rocket from liftoff until it hits the ground.

00000 00000

Numerade Educator

Problem 65

A juggler throws a ball straight up into the air with a speed of $10 \mathrm{~m} / \mathrm{s}$. With what speed would she need to throw a second ball half a second later, starting from the same position as the first, in order to hit the first ball at the top of its trajectory?

Vishal Gupta

Numerade Educator

Problem 66

A hotel elevator ascends $200 \mathrm{~m}$ with a maximum speed of $5.0 \mathrm{~m} / \mathrm{s} .$ Its acceleration and deceleration both have a magnitude of $1.0 \mathrm{~m} / \mathrm{s}^{2}$
a. How far does the elevator move while accelerating to full speed from rest?
b. How long does it take to make the complete trip from bottom to top?

Mayukh Banik

Numerade Educator

Problem 67

A car starts from rest at a stop sign. It accelerates at $2.0 \mathrm{~m} / \mathrm{s}^{2}$ for 6.0 seconds, coasts for $2.0 \mathrm{~s}$, and then slows down at a rate of $1.5 \mathrm{~m} / \mathrm{s}^{2}$ for the next stop sign. How far apart are the stop signs?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 68

A toy train is pushed forward and released at $x_{\mathrm{i}}=2.0 \mathrm{~m}$ with a speed of $2.0 \mathrm{~m} / \mathrm{s}$. It rolls at a steady speed for $2.0 \mathrm{~s}$, then one wheel begins to stick. The train comes to a stop $6.0 \mathrm{~m}$ from the point at which it was released. What is the train's acceleration after its wheel begins to stick?

00000 00000

Numerade Educator

Problem 69

Heather and Jerry are standing on a bridge $50 \mathrm{~m}$ above a river. Heather throws a rock straight down with a speed of 20 $\mathrm{m} / \mathrm{s}$. Jerry, at exactly the same instant of time, throws a rock straight up with the same speed. Ignore air resistance.
a. How much time elapses between the first splash and the second splash?
b. Which rock has the faster speed as it hits the water?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 70

A motorist is driving at $20 \mathrm{~m} / \mathrm{s}$ when she sees that a traffic light $200 \mathrm{~m}$ ahead has just turned red. She knows that this light stays red for $15 \mathrm{~s}$, and she wants to reach the light just as it turns green again. It takes her $1.0 \mathrm{~s}$ to step on the brakes and begin slowing at a constant deceleration. What is her speed as she reaches the light at the instant it turns green?

Vishal Gupta

Numerade Educator

Problem 71

A "rocket car" is launched along a long straight track at $t=0 \mathrm{~s}$. It moves with constant acceleration $a_{1}=2.0 \mathrm{~m} / \mathrm{s}^{2} .$ At $t=2.0 \mathrm{~s},$ a second car is launched along a parallel track, from the same starting point, with constant acceleration $a_{2}=8.0 \mathrm{~m} / \mathrm{s}^{2}$.
a. At what time does the second car catch up with the first one?
b. How far have the cars traveled when the second passes the first?

Hubert Agamasu

Numerade Educator

Problem 72

A Porsche challenges a Honda to a $400 \mathrm{~m}$ race. Because the Porsche's acceleration of $3.5 \mathrm{~m} / \mathrm{s}^{2}$ is larger than the Honda's $3.0 \mathrm{~m} / \mathrm{s}^{2},$ the Honda gets a $50-\mathrm{m}$ head start. Assume, somewhat unrealistically, that both cars can maintain these accelerations the entire distance. Who wins, and by how much time?

Hubert Agamasu

Numerade Educator

Problem 73

The minimum stopping distance for a car traveling at a speed of $30 \mathrm{~m} / \mathrm{s}$ is $60 \mathrm{~m}$, including the distance traveled during the driver's reaction time of $0.50 \mathrm{~s}$.
a. What is the minimum stopping distance for the same car traveling at a speed of $40 \mathrm{~m} / \mathrm{s} ?$
b. Draw a position-versus-time graph for the motion of the car in part a. Assume the car is at $x_{\mathrm{i}}=0 \mathrm{~m}$ when the driver first sees the emergency situation ahead that calls for a rapid halt.

Hubert Agamasu

Numerade Educator

Problem 74

A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket. The bolt hits the ground 6.0 s later. What was the rocket's acceleration?

Mayukh Banik

Numerade Educator

Problem 75

Objects in free fall on the earth have acceleration $a_{v}=-9.8 \mathrm{~m} / \mathrm{s}^{2} .$ On the moon, free-fall acceleration is approximately $1 / 6$ of the acceleration on earth. This changes the scale of problems involving free fall. For instance, suppose you jump straight upward, leaving the ground with velocity $v_{i}$ and then steadily slowing until reaching zero velocity at your highest point. Because your initial velocity is determined mostly by the strength of your leg muscles, we can assume your initial velocity would be the same on the moon. But considering the final equation in Table 2.4 we can see that, with a smaller free-fall acceleration, your maximum height would be greater. The following questions ask you to think about how certain athletic feats might be performed in this reduced-gravity environment.
If an astronaut can jump straight up to a height of $0.50 \mathrm{~m}$ on earth, how high could he jump on the moon?
A. $1.2 \mathrm{~m}$
B. $3.0 \mathrm{~m}$
C. $3.6 \mathrm{~m}$
D. $18 \mathrm{~m}$

Hubert Agamasu

Numerade Educator

Problem 76

Objects in free fall on the earth have acceleration $a_{v}=-9.8 \mathrm{~m} / \mathrm{s}^{2} .$ On the moon, free-fall acceleration is approximately $1 / 6$ of the acceleration on earth. This changes the scale of problems involving free fall. For instance, suppose you jump straight upward, leaving the ground with velocity $v_{i}$ and then steadily slowing until reaching zero velocity at your highest point. Because your initial velocity is determined mostly by the strength of your leg muscles, we can assume your initial velocity would be the same on the moon. But considering the final equation in Table 2.4 we can see that, with a smaller free-fall acceleration, your maximum height would be greater. The following questions ask you to think about how certain athletic feats might be performed in this reduced-gravity environment.
On the earth, an astronaut can safely jump to the ground from a height of $1.0 \mathrm{~m}$; her velocity when reaching the ground is slow enough to not cause injury. From what height could the astronaut safely jump to the ground on the moon?
A. $2.4 \mathrm{~m}$
B. $6.0 \mathrm{~m}$
C. $7.2 \mathrm{~m}$
D. $36 \mathrm{~m}$

Hubert Agamasu

Numerade Educator

Problem 77

Objects in free fall on the earth have acceleration $a_{v}=-9.8 \mathrm{~m} / \mathrm{s}^{2} .$ On the moon, free-fall acceleration is approximately $1 / 6$ of the acceleration on earth. This changes the scale of problems involving free fall. For instance, suppose you jump straight upward, leaving the ground with velocity $v_{i}$ and then steadily slowing until reaching zero velocity at your highest point. Because your initial velocity is determined mostly by the strength of your leg muscles, we can assume your initial velocity would be the same on the moon. But considering the final equation in Table 2.4 we can see that, with a smaller free-fall acceleration, your maximum height would be greater. The following questions ask you to think about how certain athletic feats might be performed in this reduced-gravity environment.
On the earth, an astronaut throws a ball straight upward; it stays in the air for a total time of $3.0 \mathrm{~s}$ before reaching the ground again. If a ball were to be thrown upward with the same initial speed on the moon, how much time would pass before it hit the ground?
A. $7.3 \mathrm{~s}$
B. $18 \mathrm{~s}$
C. $44 \mathrm{~s}$
D. $108 \mathrm{~s}$

Hubert Agamasu

Numerade Educator