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College Physics 2017

Raymond A. Serway, Chris Vuille, John hughes

Chapter 2

Motion in One Dimension

Educators


Problem 1

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

Averell H.
Carnegie Mellon University

Problem 2

Light travels at a speed of about $3 \times 10^{3} \mathrm{m} / \mathrm{s}$ . (a) 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? (b) Compare this distance to the diameter of Earth.

Averell H.
Carnegie Mellon University

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 min at 80.0 km/h, 12.0 min at 100 km/h, and 45.0 min at 40.0 km/h and spends 15.0 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 H.
Carnegie Mellon University

Problem 4

A football player runs from his own goal line to the opposing team’s goal line, returning to the fifty-yard line, all in 18.0 s. Calculate (a) his average speed, and (b) the magnitude of his average velocity.

Averell H.
Carnegie Mellon University

Problem 5

Two boats start together and race across a 60-km-wide lake and back. Boat A goes across at 60 km/h and returns at 60 km/h. Boat B goes across at 30 km/h, and its crew, realizing how far behind it is getting, returns at 90 km/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 H.
Carnegie Mellon University

Problem 6

A graph of position versus time for a certain particle moving along the x - axis is shown in Figure P2.6. Find the average velocity in the time intervals from (a) 0 to 2.00 s, (b) 0 to 4.00 s, (c) 2.00 s to 4.00 s, (d) 4.00 s to 7.00 s, and (e) 0 to 8.00 s.

Averell H.
Carnegie Mellon University

Problem 7

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

Averell H.
Carnegie Mellon University

Problem 8

A tennis player moves in a straight-line path as shown in Figure P2.8. Find her average velocity in the time intervals from (a) 0 to 1.0 s, (b) 0 to 4.0 s, (c) 1.0 s to 5.0 s, and (d) 0 to 5.0 s.

Averell H.
Carnegie Mellon University

Problem 9

A jet plane has a takeoff speed of $v_{10}=75 {m} / {s}$ and can move along the runway at an average acceleration of 1.3 ${m} / {s}^{2} .$ If the length of the runway is $2.5 {km},$ will the plane be able to use this runway safely? Defend your answer.

Averell H.
Carnegie Mellon University

Problem 10

Two cars travel in the same direction along a straight highway, one at a constant speed of 55 mi/h and the other at 70 mi/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?

Averell H.
Carnegie Mellon University

Problem 11

The cheetah can reach a top speed of 114 km/h (71 mi/h). While chasing its prey in a short sprint, a cheetah starts from rest and runs 45 m in a straight line, reaching a final speed of 72 km/h. (a) Determine the cheetah’s average acceleration during the short sprint, and (b) find its displacement at t 5 3.5 s.

Averell H.
Carnegie Mellon University

Problem 12

En 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?

Averell H.
Carnegie Mellon University

Problem 13

A person takes a trip, driving with a constant speed of 89.5 km/h, except for a 22.0-min rest stop. If the person’s average speed is 77.8 km/h, (a) how much time is spent on the trip and (b) how far does the person travel?

Averell H.
Carnegie Mellon University

Problem 14

A tortoise can run with a speed of 0.10 m/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 cm). (a) How long does the race take? (b) What is the length of the race?

Averell H.
Carnegie Mellon University

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 $1.60 \times 10^{3}$ . If a particular car covers the first half of the track at an average speed of 230. km/h, what minimum average speed must it have in the second half of the event to qualify?

Averell H.
Carnegie Mellon University

Problem 16

A paper in the journal Current Biology tells of some jellyfish-like animals that attack their prey by launching stinging cells in one of the animal kingdom’s fastest movements. High-speed photography showed the cells were accelerated from rest for 700 . ns at $5.30 \times 10^{7} {m} / {s}^{2}$ . Calculate (a) the maximum speed reached by the cells and (b) the distance traveled during the acceleration.

Averell H.
Carnegie Mellon University

Problem 17

A graph of position versus time for a certain particle moving along the x - axis is shown in Figure P2.6. Find the instantaneous velocity at the instants (a) t 5 1.00 s, (b) t 5 3.00 s, (c) t 5 4.50 s, and (d) t 5 7.50 s.

Averell H.
Carnegie Mellon University

Problem 18

A race car moves such that its position fits the relationship
$$x=(5.0 {m} / {s}) t+\left(0.75 {m} / {s}^{3}\right) t^{3}$$
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 5 4.0 s, using time intervals of 0.40 s, 0.20 s, and 0.10 s. (c) Compare the average velocity during the first 4.0 s with the results of part (b).

Averell H.
Carnegie Mellon University

Problem 19

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

Averell H.
Carnegie Mellon University

Problem 20

V A particle starts from rest and accelerates as shown in Figure P2.20. Determine (a) the particle’s speed at t 5 10.0 s and at t 5 20.0 s, and (b) the distance traveled in the first 20.0 s.

Averell H.
Carnegie Mellon University

Problem 21

A 50.0-g Super Ball traveling at 25.0 m/s bounces off a brick wall and rebounds at 22.0 m/s. A highspeed camera records this event. If the ball is in contact with the wall for 3.50 ms, what is the magnitude of
the average acceleration of the ball during this time interval?

Averell H.
Carnegie Mellon University

Problem 22

BIO The average person passes out at an acceleration of 7g (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!)

Averell H.
Carnegie Mellon University

Problem 23

V A certain car is capable of accelerating at a rate of 0.60 m/s2 .How long does it take for this car to go from a speed of 55 mi/h to a speed of 60 mi/h?

Averell H.
Carnegie Mellon University

Problem 24

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

Averell H.
Carnegie Mellon University

Problem 25

A steam catapult launches a jet aircraft from the aircraft carrier John C. Stennis, giving it a speed of 175 mi/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 H.
Carnegie Mellon University

Problem 26

Solve Example 2.5, “Car Chase,” by a graphical method. On the same graph, plot position versus time for the car and the trooper. From the intersection of the two curves, read the time at which the trooper overtakes the car.

Vipin B.
Numerade Educator

Problem 27

T An object moving with uniform acceleration has a velocity of 12.0 cm/s in the positive x - direction when its x - coordinate is 3.00 cm. If its x - coordinate 2.00 s later is 25.00 cm, what is its acceleration?

Averell H.
Carnegie Mellon University

Problem 28

V 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 km/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 ${m} / {s}^{2}$ .

Averell H.
Carnegie Mellon University

Problem 29

A truck covers 40.0 m in 8.50 s while uniformly slowing down to a final velocity of 2.80 m/s. (a) Find the truck’s original speed. (b) Find its acceleration.

Averell H.
Carnegie Mellon University

Problem 30

A speedboat increases its speed uniformly from $v_{i}=20.0$ ${m} / {s}$ to $v_{f}=30.0 {m} / {s}$ in a distance of $2.00 \times 10^{2} {m} .$ (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 $v_{f}, v_{i},$ and $\Delta x$ (d) Substitute given values, obtaining that acceleration. (e) Find the time it takes the boat to travel the given distance.

Averell H.
Carnegie Mellon University

Problem 31

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

Averell H.
Carnegie Mellon University

Problem 32

An object moves with constant acceleration 4.00 $\mathrm{m} / \mathrm{s}^{2}$ and over a time interval reaches a final velocity of 12.0 m/s. (a) If its original velocity is 6.00 m/s, what is its displacement during the time interval? (b) What is the distance it travels during this interval? (c) If its original velocity is 26.00 m/s, what is its displacement during this interval? (d) What is the total distance
it travels during the interval in part (c)?

Averell H.
Carnegie Mellon University

Problem 33

In a test run, a certain car accelerates uniformly from zero to 24.0 m/s in 2.95 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 m/s to 20.0 m/s? (c) Will doubling the time always double the change in speed? Why?

Averell H.
Carnegie Mellon University

Problem 34

A jet plane lands with a speed of 100 m/s and can accelerate at a maximum rate of $-5.00 {m} / {s}^{2}$ 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 km long?

Averell H.
Carnegie Mellon University

Problem 35

Speedy Sue, driving at 30.0 m/s, enters a one-lane tunnel. She then observes a slow-moving van 155 m ahead traveling at 5.00 m/s. Sue applies her brakes but can accelerate only at $-2.00 {m} / {s}^{2}$ 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.

Prashant B.
Numerade Educator

Problem 36

A record of travel along a straight path is as follows:
1. Start from rest with a constant acceleration of 2.77 ${m} / {s}^{2}$ for 15.0 s.
2. Maintain a constant velocity for the next 2.05 min.
3. Apply a constant negative acceleration of 29.47${m} / {s}^{2}$ for 4.39 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?

Averell H.
Carnegie Mellon University

Problem 37

A train is traveling down a straight track at 20 m/s when the engineer applies the brakes, resulting in an acceleration of 21.0 ${m} / {s}^{2}$ as long as the train is in motion. How far does the train move during a 40-s time interval starting at the instant the brakes are applied?

Averell H.
Carnegie Mellon University

Problem 38

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

Guilherme B.
Numerade Educator

Problem 39

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

Averell H.
Carnegie Mellon University

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 docs the car travel? Answers are in terms of the variables $a_{1}, a_{2}, t_{1},$ and $t_{2}$

Averell H.
Carnegie Mellon University

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 m/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 m. She spends 5.00 s in the pit and then accelerates out,
reaching her previous speed of 71.5 m/s after a distance of 350 m. At this point, how far has the Thunderbird fallen behind the Mercedes Benz, which has continued at a constant speed?

Averell H.
Carnegie Mellon University

Problem 42

The kinematic equations can describe phenomena other than motion through space and time. Suppose x represents a person’s bank account balance. The units of x would be dollars ($), and velocity v would give the rate at which the balance changes (in units of, for example, $/month). Acceleration would give the rate at which v changes. Suppose a person begins with ten thousand dollars in the bank. Initial money management leads to no net change in the account balance so that v0 5 0. Unfortunately, management worsens over time so that $a=-2.5 \times 10^{2} \$ /$ month $^{2}$ . Assuming $a$ is constant, find the amount of time in months until the bank account is empty.

Averell H.
Carnegie Mellon University

Problem 43

T A hockey player is standing on his skates on a frozen pond when an opposing player, moving with a uniform speed of 12 m/s, skates by with the puck. After 3.0 s, the first player makes up his mind to chase his opponent. If he accelerates uniformly at 4.0 ${m} / {s}^{2}$ (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.)

Averell H.
Carnegie Mellon University

Problem 44

A train $4.00 \times 10^{2} {m}$ long is moving on a straight track with a speed of 82.4 ${km} / {h}$ . The engineer applies the brakes at a crossing, and later the last car passes the crossing with a speed of 16.4 km/h. Assuming constant acceleration, determine how long the train blocked the crossing. Disregard the width of the crossing.

Averell H.
Carnegie Mellon University

Problem 45

A ball is thrown vertically upward with a speed of 25.0 m/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 H.
Carnegie Mellon University

Problem 46

V A ball is thrown directly downward with an initial speed of 8.00 m/s, from a height of 30.0 m. After what time interval does it strike the ground?

Averell H.
Carnegie Mellon University

Problem 47

A certain freely falling object, released from rest, requires 1.50 s to travel the last 30.0 m before it hits the ground. (a) Find the velocity of the object when it is 30.0 m above the ground. (b) Find the total distance the object travels during the fall.

Averell H.
Carnegie Mellon University

Problem 48

An attacker at the base of a castle wall 3.65 m high throws a rock straight up with speed 7.40 m/s at a height of 1.55 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 m/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.

Averell H.
Carnegie Mellon University

Problem 49

BIO Traumatic brain injury such as concussion results when the head undergoes a very large acceleration. Generally, an acceleration less than 800 ${m} / {s}^{2}$ lasting for any length of time will not cause injury, whereas an acceleration greater than 1000 ${m} / {s}^{2}$ lasting for at least 1 ${ms}$ will cause injury. Suppose a small child rolls off a bed that is 0.40 m above the floor. If the floor is hardwood, the child’s head is brought to rest in approximately 2.0 mm. If the floor is carpeted, this stopping distance is increased to about 1.0 cm. Calculate the magnitude and duration of the deceleration in both cases, to determine the risk of injury. Assume the child remains horizontal during the fall to the floor. Note that a more complicated fall could result in a head velocity greater or less than the speed you calculate.

Averell H.
Carnegie Mellon University

Problem 50

A small mailbag is released from a helicopter that is descending steadily at 1.50 m/s. After 2.00 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 m/s?

Averell H.
Carnegie Mellon University

Problem 51

A tennis player tosses a tennis ball straight up and then catches it after 2.00 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 H.
Carnegie Mellon University

Problem 52

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

Averell H.
Carnegie Mellon University

Problem 53

A model rocket is launched straight upward with an initial speed of 50.0 m/s. It accelerates with a constant upward acceleration of 2.00 ${m} / {s}^{2}$ until its engines stop at an altitude of 150. 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 A.
Numerade Educator

Problem 54

V A baseball is hit so that it travels straight upward after being struck by the bat. A fan observes that it takes 3.00 s for the ball to reach its maximum height. Find (a) the ball’s initial velocity and (b) the height it reaches.

Averell H.
Carnegie Mellon University

Problem 55

A truck tractor pulls two trailers, one behind the other, at a constant speed of $1.00 \times 10^{2} {km} / {h}$ . It takes 0.600 ${s}$ s for the big rig to completely pass onto a bridge $4.00 \times 10^{2} {m}$ long. For what duration of time is all or part of the truck-trailer combination on the bridge?

Averell H.
Carnegie Mellon University

Problem 56

T Colonel John P. Stapp, USAF, participated in studying whether a jet pilot could survive emergency ejection. On March 19, 1954, he rode a rocket-propelled sled that moved down a track at a speed of 632 mi/h (see Fig. P2.56). He and the sled were safely brought to rest in 1.40 s. Determine in SI units (a) the negative acceleration he experienced and (b) the distance he traveled during this negative acceleration.

Averell H.
Carnegie Mellon University

Problem 57

A bullet is fired through a board 10.0 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 $4.00 \times 10^{2} {m} / {s}$ and it emerges from the other side of the board with a speed of $3.00 \times 10^{2} {m} / {s}$ , 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.

Averell H.
Carnegie Mellon University

Problem 58

A speedboat moving at 30.0 ${m} / {s}$ approaches a no-wake buoy marker $1.00 \times 10^{2} {m}$ ahead. The pilot slows the boat with a constant acceleration of $-3.50 {m} / {s}^{2}$ 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?

Averell H.
Carnegie Mellon University

Problem 59

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

Averell H.
Carnegie Mellon University

Problem 60

BIO Mature salmon swim upstream, returning to spawn at their birthplace. During the arduous trip they leap vertically upward over waterfalls as high as 3.6 m. With what minimum speed must a salmon launch itself into the air to clear a 3.6 - m waterfall?

Averell H.
Carnegie Mellon University

Problem 61

An insect called the froghopper (Philaenus spumarius) has been called the best jumper in the animal kingdom. This insect can accelerate at over $4.0 \times 10^{3} {m} / {s}^{2}$ during a displacement of 2.0 mm as it straightens its specially equipped “jumping legs.” (a) Assuming uniform acceleration, what is the insect’s speed after it has accelerated through this short distance? (b) How long does it take to reach that speed? (c) How high could the insect jump if air resistance could be ignored? Note that the actual height obtained is about 0.70 m, so air resistance is important here.

Averell H.
Carnegie Mellon University

Problem 62

An object is moving in the positive direction along the x - axis. Sketch plots of the object’s position vs. time and velocity vs. time if (a) its speed is constant, (b) it’s speeding up at a constant rate, and (c) it’s slowing down at a constant rate.

Averell H.
Carnegie Mellon University

Problem 63

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

Averell H.
Carnegie Mellon University

Problem 64

A player holds two baseballs a height $h$ above the ground. He throws one ball vertically upward at speed $v_{0}$ and the other vertically downward at the same speed. Calculate (a) the speed of each ball as it hits the ground and (b) the difference between their times of flight.

Averell H.
Carnegie Mellon University

Problem 65

A ball thrown straight up into the air is found to be moving at 1.50 m/s after rising 2.00 m above its release point. Find the ball’s initial speed.

Averell H.
Carnegie Mellon University

Problem 66

BIO The thickest and strongest chamber in the human heart is the left ventricle, responsible during systole for pumping oxygenated blood through the aorta to rest of the body. Assume aortic blood starts from rest and accelerates at 22.5 ${m} / {s}^{2}$ to a peak speed of 1.05 ${m} / {s}$ . (a) How far does the blood travel during this acceleration? (b) How much time is required for the blood to reach its peak speed?

Averell H.
Carnegie Mellon University

Problem 67

Emily challenges her husband, David, to catch a $1 bill as follows. She holds the bill vertically as in Figure P2.67, 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 s, will he succeed? Explain your reasoning. (This challenge is a good trick you might want to try with your friends.)

Averell H.
Carnegie Mellon University

Problem 68

A mountain climber stands at the top of a 50.0 - m cliff that overhangs a calm pool of water. She throws two stones vertically downward 1.00 s apart and observes that they cause a single splash. The first stone had an initial velocity of 22.00 m/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?

Averell H.
Carnegie Mellon University

Problem 69

One of Aesop’s fables tells of a race between a tortoise and a hare. Suppose the overconfident hare takes a nap and wakes up to find the tortoise a distance d ahead and a distance L from the finish line. If the hare then begins running with constant speed $v_{1}$ and the tortoise continues crawling with constant speed $v_{2},$ it turns out that the tortoise wins the race if the distance $L$ is less than $\left(v_{2} /\left(v_{1}-v_{2}\right)\right) d$ . Obtain this result by first writing expressions for the times taken by the hare and the tortoise to finish the race, and then noticing that to win, $t_{\text { tortoise }}<t_{\text { lare }},$ Assume $v_{2}<v_{1}$

Averell H.
Carnegie Mellon University

Problem 70

In Bosnia, the ultimate test of a young man’s courage used to be to jump off a 400 - year - old bridge (destroyed in 1993; rebuilt in 2004) into the River Neretva, 23 m below the bridge. (a) How long did the jump last? (b) How fast was the jumper traveling upon impact with the river? (c) If the speed of sound
in air is 340 m/s, how long after the jumper took off did a spectator on the bridge hear the splash?

Averell H.
Carnegie Mellon University

Problem 71

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 m/s, and the man is initially 3.00 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 H.
Carnegie Mellon University