Chapter Three

A projectile is fired horizontally with an initial speed of 50.0 m/s. Neglect air resistance. What is the speed of the projectile 3.00 s after it is fired?

50.0 m/s

A GPS tracking device is placed in a police dog to monitor its whereabouts relative to the police station. At time t1 = 23 min, the dog's displacement from the station is 1.2 km, 33° north of east. At time t2 = 57 min, the dog's displacement from the station is 2.0 km, 75° north of east. Find the magnitude and direction of the dog's average velocity between these two times.

0.67 m/s, 21° west of north

An arrow is shot horizontally from a height of 4.9 m above the ground. The initial speed of the arrow is 45 m/s. Neglecting friction, how long will it take the arrow to hit the ground?

1.0 s

A man at point A directs his rowboat due north toward point B, straight across a river of width 100 m. The river current is due east. The man starts across, rowing steadily at 0.75 m/s and reaches the other side of the river at point C, 150 m downstream from his starting point. What is the speed of the river?

1.1 m/s

A ferry can travel at an optimal speed of 8 km/h in still water measured relative to the shore. What is the optimal speed of the ferry, relative to the shore, if it moves perpendicular to a 6 km/h current?

10 km/h

During a one-hour trip, a small boat travels 80.0 km north and then travels 60.0 km east. What is the magnitude of the boat's average velocity for the one-hour trip?

100 km/h

Two cars A and B approach each other at an intersection. Car A is traveling south at 20 m/s, while car B is traveling east at 17 m/s. What is the velocity of car A as described by the passengers in car B?

26 m/s, 50° south of west

A basketball player is running at a constant speed of 2.5 m/s when he tosses a basketball upward with a speed of 6.0 m/s. How far does the player run before he catches the ball? Ignore air resistance.

3.1 m

A football is kicked with a speed of 18 m/s at an angle of 65° to the horizontal. How long is the football in the air? Neglect air resistance.

3.3 s

A physics student standing on the edge of a cliff throws a stone vertically downward with an initial speed of 10.0 m/s. The instant before the stone hits the ground below, it is traveling at a speed of 30.0 m/s. If the physics student were to throw the rock horizontally outward from the cliff instead, with the same initial speed of 10.0 m/s, what is the magnitude of the velocity of the stone just before it hits the ground?

30.0 m/s

A tennis ball is thrown vertically with an initial speed of 20.0 m/s at time t = 0 s. Approximately, what is the initial speed of the ball relative to an observer in a car that moves horizontally past the launch location with a constant speed of 30 m/s?

36 m/s

A motorcycle has a velocity of 24 m/s, due south as it passes a car with a velocity of 15 m/s, due north. What is the magnitude and direction of the velocity of the motorcycle as seen by the driver of the car?

39 m/s, south

Two cars approach each other on a straight and level road. Car A is traveling at 75 km/h, due north and car B is traveling at 45 km/h, due south. Both velocities are measured relative to the ground. At a certain instant, the distance between the cars is 15 km. How long will it take, in seconds, from that instant for the two cars to meet?

450 s

On a two lane highway, a car is following a pickup truck. At one instant, the car has a speed of 32 m/s and is 184 m behind the truck. At the same time, the truck has a speed of 28 m/s. If neither vehicle accelerates, how long will it take the car to catch up to the truck?

46 s

A spaceship is observed traveling in the positive x direction with a speed of 150 m/s when it begins accelerating at a constant rate. The spaceship is observed 25 s later traveling with an instantaneous velocity of 1500 m/s at an angle of 55° above the +x axis. What was the magnitude of the acceleration of the spaceship during the 25 seconds?

57 m/s2

A rock is kicked horizontally at a speed of 15 m/s from the edge of a cliff. The rock strikes the ground 65 m from the foot of the cliff of height H as suggested in the figure, which is not drawn to scale. Neglect air resistance. What is the approximate value of H, the height of the cliff?

78 m

A tennis ball is thrown upward at an angle from point A. It follows a parabolic trajectory and hits the ground at point D. At the instant shown, the ball is at point B. Point C represents the highest position of the ball above the ground. At which point is the velocity vector changing most rapidly with time?

It is changing at the same rate at all four points.

A tennis ball is thrown upward at an angle from point A. It follows a parabolic trajectory and hits the ground at point D. At the instant shown, the ball is at point B. Point C represents the highest position of the ball above the ground. Which statement is true concerning the ball when it is at C, the highest point in its trajectory?

The ball's velocity is perpendicular to its acceleration.

A spring-loaded gun is aimed horizontally and is used to launch identical balls with different initial speeds. The gun is at a fixed position above the floor. The balls are fired one at a time. If the speed of the second ball fired is twice the speed of the first ball fired, how is the horizontal range (denoted R in the figure) affected?

The range of the second ball will be twice as large as that of the first ball.

A tennis ball is thrown upward at an angle from point A. It follows a parabolic trajectory and hits the ground at point D. At the instant shown, the ball is at point B. Point C represents the highest position of the ball above the ground. While in flight, how do the x and y components of the velocity vector of the ball compare at the points A and D?

The velocity components have the same magnitudes at both points, but the directions of the y components are reversed.

A boat that can travel at 4.0 km/h in still water crosses a river with a current of 2.0 km/h. At what angle must the boat be pointed upstream (that is, relative to its actual path) to go straight across the river?

30°

A car travels due east at 22 m/s. It makes a turn due south and continues to travel at 22 m/s. What is the change in velocity of the car?

31 m/s, 45° south of west

Airplane One flies due east at 250 km/h relative to the ground. At the same time, Airplane Two flies 325 km/h, 35° north of east relative to the ground. What is the velocity of Airplane One relative to Airplane Two?

190 km/h, 85° south of west

A train travels due south at 60 m/s. It reverses its direction and travels due north at 60 m/s. What is the change in velocity of the train?

120 m/s, due north

A projectile is fired at an angle of 55.0° above the horizontal with an initial speed of 35.0 m/s. How long does it take the projectile to reach the highest point in its trajectory?

2.4 s

Two cars approach each other on a straight and level road. Car A is traveling at 75 km/h, due north and car B is traveling at 45 km/h, due south. Both velocities are measured relative to the ground. What is the velocity of car A relative to an observer in car B?

120 km/h, north

During a one-hour trip, a small boat travels 80.0 km north and then travels 60.0 km east. What is the boat's average speed during the one-hour trip?

140 km/h

A projectile is fired horizontally with an initial speed of 50.0 m/s. Neglect air resistance. What is the magnitude of the displacement of the projectile 3.00 s after it is fired?

156 m

A quarterback throws a pass at an angle of 35° above the horizontal with an initial speed of 25 m/s. The ball is caught by the receiver 2.55 seconds later. Determine the distance the ball was thrown. A projectile is fired horizontally with an initial speed of 57 m/s. What are the horizontal and vertical components of its displacement 3.0 s after it is fired?

52 m

During a one-hour trip, a small boat travels 80.0 km north and then travels 60.0 km east. What is the direction of the boat's average velocity for the one-hour trip?

53.1° north of east

During football practice, a football is kicked with a speed of 22 m/s at an angle of 60.0° relative to the positive x direction. At that instant, an observer rides past the football in a car that moves with a constant speed of 11 m/s in the positive x direction. Determine the initial velocity of the ball relative to the observer in the car.

19 m/s in the +y direction

During football practice, a football is kicked with a speed of 22 m/s at an angle of 60.0° relative to the positive x direction. At that instant, an observer rides past the football in a car that moves with a constant speed of 11 m/s in the positive x direction. Complete the following statement: According to the observer in the car, the ball will

follow a path that is straight up and down in the y direction.

A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. What is the speed of the projectile when it is at the highest point in its trajectory?

30 m/s

A shell is fired with a horizontal velocity in the positive x direction from the top of an 80-m high cliff. The shell strikes the ground 1330 m from the base of the cliff. The drawing is not to scale. What is the magnitude of the velocity of the shell as it hits the ground?

330 m/s

A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. Approximately how long does it take the projectile to reach the highest point in its trajectory?

4 s

A delivery truck leaves a warehouse and travels 2.60 km north. The truck makes a left turn and travels 1.25 km west before making another right turn to travel 1.40 km north to arrive at its destination. What is the magnitude and direction of the truck's displacement from the warehouse?

4.19 km, 72.6° north of west

A basketball is launched with an initial speed of 8.0 m/s and follows the trajectory shown. The ball enters the basket 0.96 s after it is launched. What are the distances x and y? Note: The drawing is not to scale.

X: 5.4 m Y: 0.91 m

A tennis ball is thrown upward at an angle from point A. It follows a parabolic trajectory and hits the ground at point D. At the instant shown, the ball is at point B. Point C represents the highest position of the ball above the ground. While in flight, how do the x and y components of the velocity vector of the ball compare at the points B and C?

The x components are the same; the y component at C is zero m/s

A baseball is hit upward and travels along a parabolic arc before it strikes the ground. Which one of the following statements is necessarily true?

The x-component of the velocity of the ball is the same throughout the ball's flight.

A cannonball at ground level is aimed 30.0° above the horizontal and is fired with an initial speed of 125 m/s. How far away from the cannon will the cannonball hit the ground?

1380 m

An eagle is flying due east at 8.9 m/s carrying a gopher in its talons. The gopher manages to break free at a height of 12 m. What is the magnitude of the gopher's velocity as it reaches the ground? Note: effects of air resistance are not included in this calculation.

18 m/s

A ball is fired at an angle of 45°, the angle that yields the maximum range in the absence of air resistance. What is the ratio of the ball's maximum height to its range?

0.25

A tennis ball is thrown from ground level with velocity directed 30° above the horizontal. If it takes the ball 0.5 s to reach the top of its trajectory, what is the magnitude of the initial velocity?

4.9 m/s

A man at point A directs his rowboat due north toward point B, straight across a river of width 100 m. The river current is due east. The man starts across, rowing steadily at 0.75 m/s and reaches the other side of the river at point C, 150 m downstream from his starting point. While the man is crossing the river, what is his velocity relative to the shore?

1.35 m/s, 34° north of east

A spaceship is observed traveling in the positive x direction with a speed of 150 m/s when it begins accelerating at a constant rate. The spaceship is observed 25 s later traveling with an instantaneous velocity of 1500 m/s at an angle of 55° above the +x axis. What was the magnitude of the displacement of the spaceship during the 25 seconds?

2.0 × 104 m

At time t = 0 s, a puck is sliding on a horizontal table with a velocity 3.60 m/s, 35.0° above the +x axis. As the puck slides, a constant acceleration acts on it that has the following components: ax = -0.360 m/s2 and ay = -0.980 m/s2. What is the velocity of the puck at time t = 1.50 s?

2.48 m/s, 13.9° above the +x axis

A football is kicked with a speed of 18 m/s at an angle of 65° to the horizontal. How far does the football travel horizontally before it hits the ground?

25 m

A shell is fired with a horizontal velocity in the positive x direction from the top of an 80-m high cliff. The shell strikes the ground 1330 m from the base of the cliff. The drawing is not to scale. Determine the initial speed of the shell.

330 m/s

A car travels along a highway with a velocity of 24 m/s, west. The car exits the highway; and 4.0 s later, its instantaneous velocity is 16 m/s, 45° north of west. What is the magnitude of the average acceleration of the car during the four-second interval?

4.5 m/s2

A projectile is fired at an angle of 55.0° above the horizontal with an initial speed of 35.0 m/s. What is the magnitude of the horizontal component of the projectile's displacement at the end of 2 s?

40 m

An airplane traveling north at 400 m/s is accelerated due east at a rate of 50 m/s2 for 6 s. If the effects of air resistance and gravity are ignored, what is the final speed of the plane?

500 m/s

A bicyclist is riding at a constant speed along a straight-line path. The rider throws a ball straight up to a height a few meters above her head. Ignoring air resistance, where will the ball land?

in the same hand that threw the ball