# College Physics 2013

## Educators

### Problem 1

A car starts at rest from a stoplight and speeds up. It then moves at constant speed for a while. Then it slows down until reaching the next stoplight. Represent the motion with a motion diagram as seen by the observer on the ground.

Nicholas M.

### Problem 2

You are an observer on the ground. (a) Draw two motion diagrams representing the motions of two runners moving at the same constant speeds in opposite directions toward you. Runner 1, coming from the east, reaches you in 5 s, and runner 2 reaches you in 3 s. (b) Draw a motion of diagram for the second runner as seen by the first runner.

Nicholas M.

### Problem 3

A car is moving at constant speed on a highway. A second car catches up and passes the first car 5 s after it starts to speed up. Represent the situation with a motion diagram. Specify the observer with respect to whom you drew the diagram.

Nicholas M.

### Problem 4

A hat falls off a man’s head and lands in the snow. Draw a motion diagram representing the motion of the hat as seen by the man.

Nicholas M.

### Problem 5

You drive 100 km east, do some sightseeing, and then turn around and drive 50 km west, where you stop for lunch. (a) Represent your trip with a displacement vector. Choose an object of reference and coordinate axis so that the scalar component of this vector is (b) positive; (c) negative; (d) zero.

Nicholas M.

### Problem 6

Choose an object of reference and a set of coordinate axes associated with it. Show how two people can start and end their trips at different locations but still have the same displacement vectors in this reference frame.

Nicholas M.

### Problem 7

The scalar x-component of a displacement vector for a trip is -70 km. Represent the trip using a coordinate axis and an object of reference. Then change the axis so that the displacement component becomes +70 km.

Nicholas M.

### Problem 8

You recorded your position with respect to the front door of your house as you walked to the mailbox. Examine the data presented in Table 1.9 and answer the following questions: (a) What instruments did you use to collect data? (b) What are the uncertainties in your data? (c) Represent your motion using a position-versus-time graph. (d) Tell the story of your motion in words. (e) Show on the graph the displacement, distance, and path length.

Nicholas M.

### Problem 9

You need to determine the time interval (in seconds) needed for light to pass an atomic nucleus. What information do you need? How will you use it? What simplifying assumptions about the objects and processes do you need to make? What approximately is that time interval?

Nicholas M.

### Problem 10

A speedometer reads 65 mi/h. (a) Use as many different units as possible to represent the speed of the car. (b) If the speed-ometer reads 100 km/h, what is the car’s speed in mi/h?

Nicholas M.

### Problem 11

Convert the following record speeds so that they are in mi/h, km/h, and m/s. (a) Australian dragonfly—36 mi/h; (b) the diving peregrine falcon—349 km/h; and (c) the Lockheed SR-71 jet aircraft—980 m/s (about three times the speed of sound).

Nicholas M.

### Problem 12

EST Hair growth speed Estimate the rate that your hair grows in meters per second. Indicate any assumptions you made.

Nicholas M.

### Problem 13

A kidnapped banker looking through a slit in a van window counts her heartbeats and observes that two highway exits pass in 80 heartbeats. She knows that the distance between the exits is 1.6 km (1 mile). (a) Estimate the van’s speed. (b) Choose and describe a reference frame and draw a position-versus-time graph for the van.

Nicholas M.

### Problem 14

Make a simplified map of the path from where you live to your physics classroom. (a) Label your path and your displacement. (b) Estimate the time interval that you need to reach the classroom from where you live and your average speed.

Nicholas M.

### Problem 15

Equation Jeopardy Two observers observe two different moving objects. However, they describe their motions mathematically with the same equation: x(t) = 10 km - (4 km>h)t. (a) Write two short stories about these two motions. Specify where each observer is and what she is doing. What is happening to the moving object at t = 0? (b) Use significant digits to determine the interval within which the initial position is known.

Nicholas M.

### Problem 16

Your friend’s pedometer shows that he took 17,000 steps in 2.50 h during a hike. Determine everything you can about the hike. What assumptions did you make? How certain are you in your answer? How would the answer change if the time were given as 2.5 h instead of 2.50 h?

Nicholas M.

### Problem 17

During a hike, two friends were caught in a thunderstorm. Four seconds after seeing lightning from a distant cloud, they heard thunder. How far away was the cloud (in kilometers)? Write your answer as an interval using significant digits as your guide. Sound travels in air at about 340 m/s.

Nicholas M.

### Problem 18

Light travels at a speed of $3.0 \times 10^{8} \mathrm{m} / \mathrm{s}$ in a vacuum. The approximate distance between Earth and the Sun is $150 \times 10^{6} \mathrm{km} .$ How long it take light to travel from the Sun to Earth? What are the margins within which you know the answer?

Nicholas M.

### Problem 19

Proxima Centauri is $4.22 \pm$ 0.01 light-years from Earth. Determine the length of 1 light-year and convert the distance to the star into meters. What is the uncertainty in the answer?

Nicholas M.

### Problem 20

Spaceships traveling to other planets in the solar system move at an average speed of $1.1 \times 10^{4} \mathrm{m} / \mathrm{s} .$ It took Voyager about 12 years to reach the orbit of Uranus. What can you learn about the solar system using these data? What assumption did you make? How did this assumption affect the results?

Nicholas M.

### Problem 21

shows a velocity-versus-time graph for the bicycle trips of two friends with respect to the parking lot
where they started. (a) Determine their displacements in 20 s. (b) If Xena’s position at time zero is 0 and Gabriele’s position is 60 m, what time interval is needed for Xena to catch Gabriele? (c) Use the information from (b) to write function x(t) for Gabriele with respect to Xena.

Nicholas M.

### Problem 22

Table 1.10 shows position and time data for your walk along a straight path. (a) Tell everything you can about the walk. Specify the object of reference. (b) Draw a motion diagram, draw a graph x(t), and write a function x(t) that is consistent with the data and the chosen reference frame.

Nicholas M.

### Problem 23

Table 1.11 shows position and time data for your friend’s bicycle ride along a straight bike path. (a) Tell everything you can about his ride. Specify the observer. (b) Draw a motion diagram, draw a graph x(t), and write a function x(t) that is consistent with the ride.

Nicholas M.

### Problem 24

You are walking to your physics class at speed 1.0 m/s with respect to the ground. Your friend leaves 2.0 min after you and is walking at speed 1.3 m/s in the same direction. How fast is she walking with respect to you? How far does your friend travel before she catches up with you? Indicate the uncertainty in your answers. Describe any assumptions that you made.

Nicholas M.

### Problem 25

Gabriele enters an east–west straight bike path at the 3.0-km mark and rides west at a constant speed of 8.0 m/s. At the same time, Xena rides east from the 1.0-km mark at a constant speed of 6.0 m/s. (a) Write functions x(t) that describe their positions as a function of time with respect to Earth. (b) Where do they meet each other? In how many different ways can you solve this problem? (c) Write a function x(t) that describes Xena’s motion with respect to Gabriele.

Nicholas M.

### Problem 26

Jim is driving his car at 32 m/s (72 mi/h) along a highway where the speed limit is 25 m/s (55 mi/h). A highway patrol car observes him pass and quickly reaches a speed of 36 m/s. At that point, Jim is 300 m ahead of the patrol car. How far does the patrol car travel before catching Jim?

Nicholas M.

### Problem 27

You hike two thirds of the way to the top of a hill at a speed of 3.0 mi/h and run the final third at a speed of 6.0 mi/h. What was your average speed?

Nicholas M.

### Problem 28

Olympic champion swimmer Michael Phelps swam at an average speed of 2.01 m/s during the first half of the time needed to complete a race. What was his average swimming speed during the second half of the race if he tied the record, which was at an average speed of 2.05 m/s?

Nicholas M.

### Problem 29

A car makes a 100-km trip. It travels the first 50 km at an average speed of 50 km/h. How fast must it travel the second 50 km so that its average speed is 100 km/h?

Nicholas M.

### Problem 30

Jane and Bob see each other when 100 m apart. They are moving toward each other, Jane at speed 4.0 m/s and Bob at speed 3.0 m/s with respect to the ground. What can you determine about this situation using these data?

Nicholas M.

### Problem 31

The graph in Figure P 1.31 represents four different motions. (a) Write a function x(t) for each motion. (b) Use the information in the graph to determine as many quantities related to the motion of these objects as possible. (c) Act out these motions with two friends. (Hint: think of what each object was doing at t = 0.)

Nicholas M.

### Problem 32

A car starts from rest and reaches the speed of 10 m/s in 30 s. What can you determine about the motion of the car using this information?

Nicholas M.

### Problem 33

A truck is traveling east at $+16 m/ s$ . (a) The driver sees that the road is empty and accelerates at $+1.0 m/ s^{2}$ for 5.0 $s$ . What can you determine about the truck's motion using these data? (b) The driver then sees a red light ahead and decelerates at $-2.0 \mathrm{m} / \mathrm{s}^{2}$ for 3.0 $\mathrm{s}$ . What can you determine about the truck's motion using these data? (c) Determine the values of the quantities you listed in ( a) and (b).

Nicholas M.

### Problem 34

Bumper car collision On a bumper car ride, friends smash their cars into each other (head-on) and each has a speed change of 3.2 $m / s$ . If the magnitudes of acceleration of each car during the collision averaged 28 $m /s^{2}$ , determine the time interval needed to stop and the stopping distance for each car while colliding. Specify your reference frame.

Nicholas M.

### Problem 35

A bus leaves an intersection accelerating at $+2.0 m/ s^{2} .$ Where is the bus after 5.0 s? What assumption did you make? If this assumption is not valid, would the bus be closer or farther away from the intersection compared to your original answer? Explain.

Nicholas M.

### Problem 36

A jogger is running at +4.0 m/s when a bus passes her. The bus is accelerating from +16.0 m/s to +20.0 m/s in 8.0 s. The jogger speeds up with the same acceleration. What can you determine about the jogger’s motion using these data?

Nicholas M.

### Problem 37

The motion of a person as seen by another person is described by the equation $v=-3.0 \mathrm{m} / \mathrm{s}+\left(0.5 \mathrm{m} / \mathrm{s}^{2}\right) t .$ (a) Represent this motion with a motion diagram and position- velocity, and acceleration-versus-time graphs. (b) Say everything you can about this motion and describe what happens to the person when his speed becomes zero.

Nicholas M.

### Problem 38

Tour de France While cycling at speed of 10 $\mathrm{m} / \mathrm{s}$ , Lance Armstrong starts going downhill with an acceleration of magnitude 1.2 $\mathrm{m} / \mathrm{s}^{2} .$ The descent takes 10.0 $\mathrm{s}$ . What can you determine about Lance's motion using these data? What assumptions did you make?

Nicholas M.

### Problem 39

An automobile engineer found that the impact of a truck colliding at 16 km/h with a concrete pillar caused the bumper to indent only 6.4 cm. The truck stopped. Determine the acceleration of the truck during the collision.

Nicholas M.

### Problem 40

BIO Squid propulsion Lolliguncula brevis squid use a form of jet propulsion to swim—they eject water out of jets that can point in different directions, allowing them to change direction quickly. When swimming at a speed of 0.15 m/s or greater, they can accelerate at 1.2 $\mathrm{m} / \mathrm{s}^{2}.$ (a) Determine the time interval needed for a squid to increase its speed from
0.15 m/s to 0.45 m/s. (b) What other questions can you answer using the data?

Nicholas M.

### Problem 41

Dragster record on the desert In 1977, Kitty O’Neil drove a hydrogen peroxide–powered rocket dragster for a record time interval (3.22 s) and final speed (663 km/h) on a 402-m-long Mojave Desert track. Determine her average acceleration during the race and the acceleration while stopping (it took about 20 s to stop). What assumptions did you make?

Nicholas M.

### Problem 42

Imagine that a sprinter accelerates from rest to a maximum speed of 10.8 m/s in 1.8 s. In what time interval will he finish the 100-m race if he keeps his speed constant at 10.8 m/s for the last part of the race? What assumptions did you make?

Nicholas M.

### Problem 43

Two runners are running next to each other when one decides to accelerate at a constant rate of a. The second runner notices the acceleration after a short time interval $\Delta t$ when the distance between the runners is $\Delta x$ . The second runner accelerates at the same acceleration. Represent their motions with a motion diagram and position-versus-time graph (both graph lines on the same set of axes). Use any of the representations to predict what will happen to the distance between the runners-will it stay $\Delta x$ , increase, or decrease? Assume that the runners continue to have the same acceleration for the duration of the problem.

Nicholas M.

### Problem 44

Meteorite hits car In 1992, a 14-kg meteorite struck a car in Peekskill, NY, leaving a 20-cm-deep dent in the trunk. (a) If the meteorite was moving at 500 m/s before striking the car, what was the magnitude of its acceleration while stopping? Indicate any assumptions you made. (b) What other questions can you answer using the data in the problem?

Nicholas M.

### Problem 45

BIO Froghopper jump A spittlebug called the froghopper (Philaenus spumarius) is believed to be the best jumper in the animal world. It pushes off with muscular rear legs for 0.0010 s, reaching a speed of 4.0 m/s. Determine its acceleration during this launch and the distance that the froghopper moves while its legs are pushing.

Nicholas M.

### Problem 46

Tennis serve The fastest server in women’s tennis is Venus Williams, who recorded a serve of 130 mi/h (209 km/h) in 2007. If her racket pushed on the ball for a distance of 0.10 m, what was the average acceleration of the ball during her serve? What was the time interval for the racket-ball contact?

Nicholas M.

### Problem 47

Shot from a cannon In 1998, David “Cannonball” Smith set the distance record for being shot from a cannon (56.64 m). During a launch in the cannon’s barrel, his speed increased from zero to 80 km/h in 0.40 s. While he was being stopped by the catching net, his speed decreased from 80 km/h to zero with an average acceleration of 180 $m/ s^{2}$. What can you determine about Smith’s flight using this information?

Nicholas M.

### Problem 48

Col. John Stapp’s final sled run Col. John Stapp led the U.S. Air Force Aero Medical Laboratory’s research into the effects of higher accelerations. On Stapp’s final sled run, the sled reached a speed of 284.4 m/s (632 mi/h) and the stopped with the aid of water brakes in 1.4 s. Stapp was barely conscious and lost his vision for several days but recovered. Determine his acceleration while stopping and the distance he traveled while stopping.

Nicholas M.

### Problem 49

Sprinter Usain Bolt reached a maximum speed of 11.2 m/s in 2.0 s while running the 100-m dash. (a) What was his acceleration? (b) What distance did he travel during this first 2.0 s of the race? (c) What assumptions did you make? (d) What time interval was needed to complete the race, assuming that he ran the last part of the race at his maximum speed? (e) What is the total time for the race? How certain are you of the number you calculated?

Nicholas M.

### Problem 50

Imagine that Usain Bolt can reach his maximum speed in 1.7 s. What should be his maximum speed in order to tie the 19.5-s record for the 200-m dash?

Nicholas M.

### Problem 51

A bus is moving at a speed of 36 km/h. How far from a bus stop should the bus start to slow down so that the passengers feel comfortable (a comfortable acceleration is 1.2 $m/s^{2} ) ?$

Nicholas M.

### Problem 52

You want to estimate how fast your car accelerates. What information can you collect to answer this question? What assumptions do you need to make to do the calculation using the information?

Nicholas M.

### Problem 53

In your car, you covered 2.0 m during the first 1.0 s, 4.0 m during the second 1.0 s, 6.0 m during the third 1.0 s, and so forth. Was this motion at constant acceleration? Explain.

Nicholas M.

### Problem 54

(a) Determine the acceleration of a car in which the velocity changes from -10 m/s to -20 m/s in 4.0 s. (b) Determine the car’s acceleration if its velocity changes from -20 m/s to -18 m/s in 2.0 s. (c) Explain why the sign of the acceleration is different in (a) and (b).

Nicholas M.

### Problem 55

Use the velocity-versus-time graph lines in Figure P 1.55 to determine the change in the position of each car from 0 s to 60 s. Represent the motion of each car mathematically as a function $x(t).$ Their initial positions are A (200 m) and B (-200 m).

Nicholas M.

### Problem 56

An object moves so that its position changes in the following way: x = 10 m - (4 m>s)t. (a) Describe all of the known quantities for this motion. (b) Invent a story for the motion. (c) Draw a position-versus-time graph, and use the graph to determine when the object reaches the origin of the reference frame. (e) Act out the motion.

Nicholas M.

### Problem 57

An object moves so that its position changes in the following way: $x(t)=-100 m+(30 m/s) t+\left(3.0 m/s^{2}\right) t^{2}.$ (a) What kind of motion is this (constant velocity, constant acceleration, or changing acceleration)? (b) Describe all of the known quantities for this motion. (c) Invent a story for
the motion. (d) Draw a velocity-versus-time graph, and use it to determine when the object stops. (e) Use equations to determine when and where it stops. Did you get the same answer using graphs and equations?

Nicholas M.

### Problem 58

The position of an object changes according to the functions listed below. For each case, determine the known quantities concerning the motion, devise a story describing the motion consistent with the functions, and draw position-versus-time, velocity-versus-time, and acceleration-versus-time graphs: (a) $x(t)=15.0 \mathrm{m}-\left(-3.0 m /s^{2}\right) t^{2}$ (b) $x(t)=30.0 m-(1.0 m / s) t ;$ and $(\mathrm{c}) x=-10 \mathrm{m}$

Nicholas M.

### Problem 59

The positions of objects $A$ and $B$ with respect to Earth depend on time as follows: $x(t)_{A}=10.0 m-(4.0 m / s) t ;$ $x(t)_{B}=-12 m+(6 m /s) t .$ Represent their motions on a motion diagram and graphically (position versus-time and velocity-versus-time graphs). Use the graphical representations
to find where and when they will meet. Confirm the result with mathematics.

Nicholas M.

### Problem 60

Two cars on a straight road at time zero are beside each other. The first car, traveling at speed 30 m/s, is passing the second car, which is traveling at 24 m/s. Seeing a cow on the road ahead, the driver of each car starts to slow down at 6.0 $m/ s^{2}$. Represent the motions of the cars mathematically and on a velocity-versus-time graph from the point of view of a pedestrian. Where is each car when it stops?

Nicholas M.

### Problem 61

The changing velocity of a car is represented in the velocity-versus-time graph shown in Figure P 1.61. (a) Describe everything you can about the motion of the car using the graph. (b) What is the displacement of the car between times 10 s and 20 s? (c) What was the average speed of the car?

Nicholas M.

### Problem 62

The changing velocity of a car is represented in the velocity- versus-time graph shown in Figure P 1.62. (a) Describe everything you can about the motion of the car using the graph. (b) What is the displacement of the car between times 0 s and 45 s? What is the path traveled? (c) What is the average speed of the car during all 70 s? What is the average velocity?

Nicholas M.

### Problem 63

A diagram representing the motion of two cars is shown in Figure P 1.63. The number near each dot indicates the clock reading in seconds when the car passes that location. (a) Indicate times when the cars have the same

Nicholas M.

### Problem 64

Solve the equations below for the unknown quantities and then describe a possible process that is consistent with the equations. There are many possibilities. The object is moving on an inclined surface. This is a two-part process.

Part I: $\quad x_{1}=0+(0) t_{1}+\left(2.5 m/s^{2}\right) t_{1}^{2}$
Part II: $\quad x_{2}=x_{1}+(20 m/s)(0.40 s)+(1 / 2) a_{x 2}(0.40 s)^{2}$

Nicholas M.

### Problem 65

You accidentally drop an eraser out the window of an apartment 15 m above the ground. (a) How long will it take for the eraser to reach the ground? (b) What speed will it have just before it reaches the ground? (c) If you multiply the time interval answer from (a) and the speed answer from (b), why is the result much more than 15 m?

Nicholas M.

### Problem 66

What is the average speed of the eraser in the previous problem?

Nicholas M.

### Problem 67

You throw a tennis ball straight upward. The initial speed is about 12 m/s. Say everything you can about the motion of the ball. Is 12 m/s a realistic speed for an object that you can throw with your hands?

Nicholas M.

### Problem 68

While skydiving, your parachute opens and you slow from 50.0 m/s to 8.0 m/s in 0.80 s. Determine the distance you fall while the parachute is opening. Some people faint if they experience acceleration greater than 5 g $\left(5 \text { times } 9.8 m/ s^{2}\right) .$ Will you feel faint? Explain and discuss simplifying assumptions inherent in your explanation.

Nicholas M.

### Problem 69

After landing from your skydiving experience, you are so excited that you throw your helmet upward. The helmet rises 5.0 m above your hands. What was the initial speed of the helmet when it left your hands? How long was it moving from the time it left your hands until it returned?

Nicholas M.

### Problem 70

You are standing on the rim of a canyon. You drop a rock and in 7.0 s hear the sound of it hitting the bottom. How deep is the canyon? What assumptions did you make? Examine how each assumption affects the answer. Does it lead to a larger or smaller depth than the calculated depth? (The speed of sound in air is about 340 m/s.)

Nicholas M.

### Problem 71

You are doing an experiment to determine your reaction time. Your friend holds a ruler. You place your fingers near the sides of the lower part of the ruler without touching it. The friend drops the ruler without warning you. You catch the ruler after it falls 12.0 cm. What was your reaction time?

Nicholas M.

### Problem 72

EST Cliff divers Divers in Acapulco fall 36 m from a cliff into the water. Estimate their speed when they enter the water and the time interval needed to reach the water. What assumption did you make? Does this assumption make the calculated speed larger or smaller than actual speed?

Nicholas M.

### Problem 73

Galileo dropped a light rock and a heavy rock from the Leaning Tower of Pisa, which is about 55 m high. Suppose that Galileo dropped one rock 0.50 s before the second rock. With what initial velocity should he drop the second rock so that it reaches the ground at the same time as the first rock?

Nicholas M.

### Problem 74

A person holding a lunch bag is moving upward in a hot air balloon at a constant speed of 7.0 m/s. When the balloon is 24 m above the ground, she accidentally releases the bag. What is the speed of the bag just before it reaches the ground?

Nicholas M.

### Problem 75

A parachutist falling vertically at a constant speed of 10 m/s drops a penknife when 20 m above the ground. What is the speed of the knife just before it reaches the ground?

Nicholas M.

### Problem 76

You are traveling in your car at 20 m/s a distance of 20 m behind a car traveling at the same speed. The driver of the other car slams on the brakes to stop for a pedestrian who is crossing the street. Will you hit the car? Your reaction time is 0.60 s. The maximum acceleration of each car is 9.0 $m/ s^{2}$

Nicholas M.

### Problem 77

You are driving a car behind another car. Both cars are moving at speed 80 km/h. What minimum distance behind the car in front should you drive so that you do not crash into the car’s rear end if the driver of that car slams on the brakes? Indicate any assumptions you made.

Nicholas M.

### Problem 78

A driver with a 0.80 -s reaction time applies the brakes, causing the car to have $7.0-m/s^{2}$ acceleration opposite the direction of motion. If the car is initially traveling at 21 m/s, how far does the car travel during the reaction time? How far does the car travel after the brakes are applied and while skidding to a stop?

Nicholas M.

### Problem 79

Some people in a hotel are dropping water balloons from their open window onto the ground below. The balloons take 0.15 s to pass your 1.6-m-tall window. Where should security look for the raucous hotel guests? Indicate any assumptions that you made in your solution.

Nicholas M.

### Problem 80

BIO EST Avoiding injury from hockey puck Hockey players wear protective helmets with face masks. Why? Because the bone in the upper part of the cheek (the zygomatic bone) can fracture if the acceleration of a hockey puck due to its interaction with the bone exceeds 900 g for a time lasting 6.0 ms or longer. Suppose a player was not wearing a face mask. Is it likely that the acceleration of a hockey puck when hitting the bone would exceed these numbers? Use some reasonable numbers of your choice and estimate the puck’s acceleration if hitting an unprotected zygomatic bone.

Nicholas M.

### Problem 81

A bottle rocket burns for 1.6 s. After it stops burning, it continues moving up to a maximum height of 80 m above the place where it stopped burning. Estimate the acceleration of the rocket during launch. Indicate any assumptions made during your solution. Examine their effect.

Nicholas M.

### Problem 82

The state driver’s manual lists the reaction distances, braking distances, and total stopping distances for automobiles traveling at different initial speeds (Table 1.12). Use the data determine the driver’s
reaction time interval and the acceleration of the automobile while braking. The numbers assume dry surfaces for passenger vehicles.

Nicholas M.

### Problem 83

Estimate the time interval needed to pass a semi-trailer truck on a highway. If you are on a two-lane highway, how far away from you must an approaching car be in order for you to safely pass the truck without colliding with the oncoming traffic? Indicate any assumptions used in your estimate.

Nicholas M.

### Problem 84

Car A is heading east at 30 m/s and Car B is heading west at 20 m/s. Suddenly, as they approach each other, they see a one-way bridge ahead. They are 100 m apart when they each apply the brakes. Car A’s speed decreases at 7.0 m/s each second and Car B decreases at 9.0 m/s each second. Do the cars collide?

Nicholas M.

### Problem 85

Suppose that the magnitude of the head velocity change was 10 m/s. Which time interval below for the collision would be closest to producing a possible concussion with an acceleration of 1000 $m/s^{2} ?$

$\begin{array}{ll}{\text { (a) } 1 s} & {\text { (b) } 0.1 s} & {\text { (c) } 10^{-2} s}\\ {\text { (d) } 10^{-3} s} & {\text { (e) } 10^{-4} s}\end{array}$

Nicholas M.

### Problem 86

Using numbers from the previous problem, which answer below is closest to the average speed of the head while stopping?

$\begin{array}{ll}{\text { (a) } 50 m /s} & {\text { (b) } 10 m /s} & {\text { (c) } 5 m /s} \\ {\text { (d) } 0.5 m / s} & {\text { (e) } 0.1 m / s}\end{array}$

Nicholas M.

### Problem 87

Suppose the average speed while stopping was 4 m/s (not necessarily the correct value) and the collision lasted 0.01 s. Which answer below is closest to the head’s stopping distance (the distance it moves while stopping)?

$\begin{array}{ll}{\text { (a) } 0.04 m} & {\text { (b) } 0.4 m} & {\text { (c) } 4 m} \\ {\text { (d) } 0.02 m} & {\text { (e) } 0.004 m}\end{array}$

Nicholas M.

### Problem 88

Use Eq. (1.7) and the numbers from Problem 85 to determine which stopping distance below is closest to that which would

$\begin{array}{ll}{\text { (a) } 0.005 m} & {\text { (b) } 0.5 m} & {\text { (c) } 0.5 m} \\ {\text { (d) } 0.01 m} & {\text { (e) } 0.05 m}\end{array}$

Nicholas M.

### Problem 89

Choose from the list below the changes in the head impacts that would reduce the acceleration during the impact.

1. A shorter impact time interval
2. A longer impact time interval
3. A shorter stopping distance
4. A longer stopping distance
5. A smaller initial speed
6. A larger initial speed

(a) 1, 4, 6 (b) 1, 3, 5 (c) 1, 4, 5
(d) 2, 4, 5 (e) 2, 4, 6

Sending rockets to observe X-ray sources Before 1962, few astronomers believed that the universe contained celestial bodies that were hot enough to emit X-rays—about 10,000 times hotter than the surface of the Sun.
Because the atmosphere absorbs the X-rays produced by such sources, they can only be detected beyond Earth’s atmosphere, 200 km or more above Earth’s surface. Before satellites were available in the 1970 s, scientists searched for X-ray sources by launching rockets (the first in 1962 from White Sands Missile Range in New Mexico) that contained detectors that could sample the skies for the short time interval that the rocket remained above the atmosphere—less than 10 min. Such a Terrier-Sandhawk rocket was flown on May 11, 1970 from the Kauai Test Range in Hawaii. Modern satellites can collect data continuously. Satellite observations and analysis have now identified several types of celestial bodies that emit X-rays, including X-ray pulsars in the constellations of Cygnus and Hercules, supernovae remnants, and quasars.

Nicholas M.

### Problem 90

Detectors on rockets moving above Earth’s atmosphere can detect X-ray sources, but similar detectors on Earth cannot because

(a) light from the Sun overwhelms the X-ray signals in the detectors.
(b) air in the atmosphere absorbs the X-rays before they reach Earth-based detectors.
(c) the rocket can see the X-ray sources more easily because it is nearer them.
(d) Earth is much heaver than a rocket, and hence the X-rays affect it less.

Nicholas M.

### Problem 91

During fuel burn, the vertically launched Terrier-Sandhawk rocket had an acceleration of 300 $m/ s^{2}$(30 times free-fall acceleration—called 30 g). The fuel burned for 8 s. About how fast was the rocket moving at the end of the burn?

(a) 2400 m/s (b) 40 m/s (c) 240 g (d) 4 g

Nicholas M.

### Problem 92

Which answer below is closest to the height of the Terrier Sand hawk rocket at the end of fuel burn?

(a) 20,000 m (b) 10,000 m (c) 1000 m (d) 300 m

Nicholas M.

### Problem 93

Which number below is closest to the time interval after blast- off that the Terrier-Sandhawk rocket reached its maximum height?

(a) 19,000 s (b) 2400 s (c) 250 s (d) 10 s

Nicholas M.