Answer: On which of these hills does the ball roll down

Problem 1E What is the impact speed when a car moving at 100 km/h bumps into the rear of another car traveling in the same direction at 98 km/h?

Problem 1P You toss a ball straight up with an initial speed of 30 m/s. How high does it go, and how long is it in the air (neglecting air resistance)?

Problem 1PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. Calculate your-walking speed when you step 1 meter in 0.5 second.

Jogging Jake runs along a train flatcar that moves at the velocities shown in positions A–D. From greatest to least, rank Jake’s velocities relative to a stationary observer on the ground. (Call the direction to the right positive.)

As you read this, how fast are you moving relative to the chair you are sitting on? Relative to the Sun?

Problem 2E Suzie Surefoot can paddle a canoe in still water at 8 km/h. How successful will she be at canoeing upstream in a river that flows at 8 km/h?

Problem 2P A ball is tossed with enough speed straight up so that it is in the air several seconds. (a) What is the velocity of the ball when it reaches its highest point? (b) What is its velocity 1 s before it reaches its highest point? (c) What is the change in its velocity during this 1-s interval? (d) What is its velocity 1 s after it reaches its highest point? (e) What is the change in velocity during this 1-s interval? (f) What is the change in velocity during the 2-s interval? (Careful!) (g) What is the acceleration of the ball during any of these time intervals and at the moment the ball has zero velocity?

Problem 2PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. Calculate the speed of a bowling ball that travels 4 meters in 2 seconds.

A track is made of a piece of channel iron bent as shown. A ball released at the left end of the track continues past the various points. Rank the speed of the ball at points A, B, C, and D, from fastest to slowest. (Watch for tie scores.)

Problem 2RQ What two units of measurement are necessary for describing speed?

Problem 3E Is a fine for speeding based on ones average speed or one’s instantaneous speed? Explain.

What is the instantaneous velocity of a freely falling object 10 s after it is released from a position of rest? What is its average velocity during this 10-s interval? How far will it fall during this time?

Problem 3PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. Calculate your average speed if you run 50 meters in 10 seconds.

Problem 3R A ball is released at the left end of these different tracks. The tracks are bent from equal-length pieces of channel iron. a. From fastest to slowest, rank the speed of the ball at the right end of the track. ________________ b. From longest to shortest, rank the tracks in terms of the time for the ball to reach the end. ________________ c. From greatest to least, rank the tracks in terms of the average speed of the ball. Or do all balls have the same average speed on all three tracks?

Problem 3RQ What kind of speed is registered by an automobile speedometer—average speed or instantaneous speed?

Problem 4E One airplane travels due north at 300 km/h while another travels due south at 300 km/h. Are their speeds the same? Are their velocities the same? Explain.

Problem 4P A car takes 10 s to go from v = 0 m/s to v = 25 m/s at constant acceleration. If you wish to find the distance traveled using the equation d = 1/2 at2 what value should you use for a?

Problem 4PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. Calculate the average speed of a tennis ball that travels the full length of the court, 24 meters, in 0.5 second.

Problem 4R Three balls of different masses are thrown straight upward with initial speeds as indicated. a. From fastest to slowest, rank the speeds of the balls 1 s after being thrown. ________________ b. From greatest to least, rank the accelerations of the balls 1 s after being thrown. (Or are the accelerations the same?)

Problem 4RQ Distinguish between instantaneous speed and average speed.

Problem 5E Light travels in a straight line at a constant speed of 300,000 km/s. What is the acceleration of light?

Problem 5P Surprisingly, very few athletes can jump more than 2 feet (0.6 m) straight up. Use d = 1/2gt2 and solve for the time one spends moving upward in a 0.6-m vertical jump. Then double it for the “hang time”—the time one’s feet are off the ground.

Problem 5PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. Calculate the average speed of a cheetah that runs 140 meters in 5 seconds.

Problem 5RQ What is the average speed in kilometers per hour for a horse that gallops a distance of 15 km in a time of 30 min?

Problem 6E Can an automobile with a velocity toward the north simultaneously have an acceleration toward the south? Explain.

A dart leaves the barrel of a blowgun at a speed v. The length of the blowgun barrel is L. Assume that the acceleration of the dart in the barrel is uniform. a. Show that the dart moves inside the barrel for a time of \(\frac {2L}{v}\) b. If the dart’s exit speed is 15.0 m/s and the length of the blowgun is 1.4 m, show that the time the dart is in the barrel is 0.19 s.

Problem 6PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. Calculate the average speed (in km/h) of Larry, who runs to the store 4 kilometers away in 30 minutes.

Problem 6RQ How far does a horse travel if it gallops at an average speed of 25 km/h for 30 min?

Problem 7E You’re in a car traveling at some specified speed limit. You see a car moving at the same speed coming toward you. How fast is the car approaching you, compared with the speed limit?

Problem 7PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. Calculate the distance (in km) that Larry runs if he maintains an average speed of 8 km/h for 1 hour.

Problem 7RQ Distinguish between speed and velocity.

Problem 8E Can an object reverse its direction of travel while maintaining a constant acceleration? If so, give an example. If not, provide an explanation.

Problem 8PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. Calculate the distance you will travel if you maintain an average speed of 10 m/s for 40 seconds.

If a car moves with a constant velocity, does it also move with a constant speed?

Problem 9E For straight-line motion, how does a speedometer indicate whether or not acceleration is occurring?

Problem 9PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. Calculate the distance you will travel if you maintain an average speed of 10 km/h for one-half hour.

Problem 9RQ If a car is moving at 90 km/h and it rounds a corner, also at 90 km/h, does it maintain a constant speed? A constant velocity? Defend your answer.

Problem 10E Correct your friend who says, “The dragster rounded the curve at a constant velocity of 100 km/h.”

Problem 10PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. Calculate the acceleration of a car (in km/h·s) that can go from rest to 100 km/h in 10 s.

Problem 10RQ Distinguish between velocity and acceleration.

You are driving north on a highway. Then, without changing speed, you round a curve and drive east. (a) Does your velocity change? (b) Do you accelerate? Explain.

Problem 11PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. Calculate the acceleration of a bus that goes from 10 km/h to a speed of 50 km/h in 10 seconds.

Problem 11RQ What is the acceleration of a car that increases its velocity from 0 to 100 km/h in 10 s?

Problem 12E Jacob says acceleration is how fast you go. Emily says acceleration is how fast you get fast. They look to you for confirmation. Who’s correct?

Problem 12PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. Calculate the acceleration of a ball that starts from rest, rolls down a ramp, and gains a speed of 25 m/s in 5 seconds.

Problem 12RQ What is the acceleration of a car that maintains a constant velocity of 100 km/h for 10 s? (Why do some of your classmates who correctly answer the question 1 get this question wrong?) Question 1 What is the acceleration of a car that increases its velocity from 0 to 100 km/h in 10 s?

Problem 13E Starting from rest, one car accelerates to a speed of 50 km/h, and another car accelerates to a speed of 60 km/h. Can you say which car underwent the greater acceleration? Why or why not?

Problem 13PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. On a distant planet, a freely falling object gains speed at a steady rate of 20 m/s during each second of fall. Calculate its acceleration.

Problem 13RQ When are you most aware of motion in a moving vehicle—when it is moving steadily in a straight line or when it is accelerating? If a car moved with absolutely constant velocity (no bumps at all), would you be aware of motion?

Cite an example of something with a constant speed that also has a varying velocity. Can you cite an example of something with a constant velocity and a varying speed? Defend your answers.

Problem 14PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. Calculate the instantaneous speed (in m/s) at the 10-second mark for a car that accelerates at 2 m/s2 from a position of rest.

Problem 14RQ Acceleration is generally defined as the time rate of change of velocity. When can it be defined as the time rate of change of speed?

Problem 15E Cite an instance in which your speed could be zero while your acceleration is nonzero.

Problem 15PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. Calculate the speed (in m/s) of a skateboarder who accelerates from rest for 3 s down a ramp at an acceleration of 5 m/s2.

Problem 15RQ What did Galileo discover about the amount of speed a ball gained each second when rolling down an inclined plane? What did this say about the ball’s acceleration?

Problem 16E Cite an example of something that undergoes acceleration while moving at constant speed. Can you also give an example of something that accelerates while traveling at constant velocity? Explain.

Problem 16PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. Calculate the instantaneous speed of an apple that falls freely from a rest position and accelerates at 10 m/s2 for 1.5 s.

Problem 16RQ What relationship did Galileo discover for the velocity acquired on an incline?

Problem 17E (a) Can an object be moving when its acceleration is zero? If so, give an example. (b) Can an object be accelerating when its speed is zero? If so, give an example.

Problem 17PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. An object is dropped from rest and falls freely. After 7 s, calculate its instantaneous speed.

Problem 17RQ What relationship did Galileo discover about a ball’s acceleration and the steepness of an incline? What acceleration occurs when the plane is vertical?

Problem 18E Can you cite an example in which the acceleration of a body is opposite in direction to its velocity? If so, what is your example?

Problem 18PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. A skydiver steps from a high-flying helicopter. In the absence of air resistance, how fast would she be falling at the end of a 12-s jump?

Problem 18RQ What exactly is meant by a “freely falling” object?

Problem 19PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. On a distant planet, a freely falling object has an acceleration of 20 m/s2. Calculate the speed that an object dropped from rest on this planet acquires in 1.5 s.

Problem 19E On which of these hills does the ball roll down with increasing speed and decreasing acceleration along the path? (Use this example if you wish to explain to someone the difference between speed and acceleration.)

Problem 19RQ What is the gain in speed per second for a freely falling object?

Problem 20E Suppose that the three balls shown in Exercise 1 start simultaneously from the tops of the hills. Which one reaches the bottom first? Explain. Exercise 1 On which of these hills does the ball roll down with increasing speed and decreasing acceleration along the path? (Use this example if you wish to explain to someone the difference between speed and acceleration.)

Problem 20PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. An apple drops from a tree and hits the ground in 1.5 s. Calculate how far it falls.

Problem 20RQ What is the velocity acquired by a freely falling object 5 s after being dropped from a rest position? What is the velocity 6 s after?

Problem 21E What is the acceleration of a car that moves at a steady velocity of 100 km/h for 100 s? Explain your answer.

Problem 21PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. Calculate the vertical distance an object dropped from rest covers in 12 s of free fall.

Problem 21RQ The acceleration of free fall is about 10 m/s2. Why does the seconds unit appear twice?

Problem 22E Which is greater, an acceleration from 25 km/h to 30 km/h or one from 96 km/h to 100 km/h if both occur during the same time?

Problem 22PC These are “plug-in-the-number” type activities to familiarize yon with the equations that link the concepts of physics. They are mainly one-step substitutions and are less challenging than the Problem. On a distant planet a freely falling object has an acceleration of 20 m/s2. Calculate the vertical distance an object dropped from rest on this planet covers in 1.5 s.

Problem 22RQ When an object is thrown upward, how much speed does it lose each second?

Problem 23E Galileo experimented with balls rolling on inclined planes of various angles. What is the range of accelerations from angles 0° to 90° (from what acceleration to what)?

Problem 23 RQ What relationship between distance traveled and time did Galileo discover for accelerating objects?

Problem 24E Be picky and correct your friend who says, “In free fall, air resistance is more effective in slowing a feather than a coin.”

Problem 24RQ What is the distance fallen for a freely falling object 1 s after being dropped from a rest position? What is it 4 s after?

Problem 25E Suppose that a freely falling object were somehow equipped with a speedometer. By how much would its reading in speed increase with each second of fall?

Problem 26E Suppose that the freely falling object in the exercise 1 were also equipped with an odometer. Would the readings of distance fallen each second indicate equal or different falling distances for successive seconds? Exercise 1 Suppose that a freely falling object were somehow equipped with a speedometer. By how much would its reading in speed increase with each second of fall?

Problem 25RQ What is the effect of air resistance on the acceleration of falling objects? What is the acceleration with no air resistance?

Problem 26RQ Consider these measurements: 10 m, 10 m/s, and 10 m/s2. Which is a measure of distance, which of speed, and which of acceleration?

Problem 27E For a freely falling object dropped from rest, what is the acceleration at the end of the fifth second of fall? At the end of the tenth second of fall? Defend your answers.

Problem 28E If air resistance can be neglected, how does the acceleration of a ball that has been tossed straight upward compare with its acceleration if simply dropped?

Problem 30E Someone standing at the edge of a cliff (as in Figure 3.8) throws a ball nearly straight up at a certain speed and another ball nearly straight down with the same initial speed. If air resistance is negligible, which ball will have the greater speed when it strikes the ground below?

Problem 29E When a ballplayer throws a ball straight up, by how much does the speed of the ball decrease each second while ascending? In the absence of air resistance, by how much does it increase each second while descending? How much time is required for rising compared to falling?

Problem 31E Answer the question 1 for the case where air resistance is not negligible—where air drag affects motion. Question 1 Someone standing at the edge of a cliff (as in Figure 3.8) throws a ball nearly straight up at a certain speed and another ball nearly straight down with the same initial speed. If air resistance is negligible, which ball will have the greater speed when it strikes the ground below?

Problem 32E If you drop an object, its acceleration toward the ground is 10 m/s2. If you throw it down instead, would its acceleration after throwing be greater than 10 m/s2? Why or why not?

Problem 33E In the exercise 1, can you think of a reason why the acceleration of the object thrown downward through the air might be appreciably less than 10 m/s2? Exercise 1 If you drop an object, its acceleration toward the ground is 10 m/s2. If you throw it down instead, would its acceleration after throwing be greater than 10 m/s2? Why or why not?

While rolling balls down an inclined plane, Galileo observes that the ball rolls 1 cubit (the distance from elbow to fingertip) as he counts to 10. How far will the ball have rolled from its starting point when he has counted to 20?

Problem 35E Consider a vertically launched projectile when air drag is negligible. When is the acceleration due to gravity greater? When ascending, at the top, or when descending? Defend your answer.

Problem 36E Extend Tables 3.2 and 3.3 to include times of fall of 6 to 10 s, assuming no air resistance.

Problem 37E If it were not for air resistance, why would it be dangerous to go outdoors on rainy days?

Problem 38E As speed increases for an object in free fall, does acceleration increase also?

Problem 39E A ball tossed upward will return to the same point with the same initial speed when air resistance is negligible. When air resistance is not negligible, how does the return speed compare with its initial speed?

Problem 40E Two balls are released simultaneously from rest at the left end of equal-length tracks A and B as shown. Which ball reaches the end of its track first?

Problem 41E Refer to the pair of tracks in Exercise 1. (a) On which track is the average speed greater? (b) Why is the speed of the ball at the end of the tracks the same? Exercise 1 Two balls are released simultaneously from rest at the left end of equal-length tracks A and B as shown. Which ball reaches the end of its track first?

Problem 42E In this chapter, we studied idealized cases of balls rolling down smooth planes and objects falling with no air resistance. Suppose a classmate complains that all this attention focused on idealized cases is worthless because idealized cases simply don’t occur in the everyday world. How would you respond to this complaint? How do you suppose the author of this book would respond?

Problem 43E A person’s hang time would be considerably greater on the Moon. Why?

Problem 44E Why does a stream of water get narrower as it falls from a faucet?

Problem 45E Make up two multiple-choice questions that would check a classmate’s understanding of the distinction between velocity and acceleration.