Physics Honors Worksheet: Chapters 2, 3, and 7

One-Dimensional Kinematics:

Assume: * standard gravitational acceleration of 9.81 m/s2 [D] on the Earth* air resistance is negligible.

The space shuttle takes off from Florida and circles the Earth several times, finally landing in California. While the shuttle is in flight, a photographer travels from Florida to California to take pictures of the astronauts when they step off of the shuttle.

1) Who undergoes the greater displacement, the astronauts or the photographer?2) Who traveled the greater distance, the astronauts or the photographer?3) Who had the larger average speed?4) Who had the larger average velocity?

An airplane travels from Cupertino to Phoenix in a straight line, which is a distance of 1000 km. It travels the first 500 km at a speed of 500 km/h. It travels the second 500 km at a speed of 250 km/h.

5) What is the average of the two velocities?6) How long did the first 500 km take?7) How long did the second 500 km take?8) How long did the trip take?9) What is the average velocity for the trip?10) Is the average velocity the same as the average of the velocities?

Suppose “up” is defined as the positive direction on a baseball field.

11) If the velocity of the ball is zero, must its acceleration be zero? Give an example.12) If the ball has a positive velocity and a negative acceleration, what is happening to the velocity? Give an

example.13) If the ball has a positive acceleration, can its speed be decreasing? Give an example.

A duck is swimming around a pond as you watch it. The average velocity of the duck is zero during a certain one-minute time interval.

14) What can you say about the displacement of the duck during that time interval?15) What can you say about the average speed of the duck?16) What can you say about the distance it travels?

You may have heard the story about the boy who traveled through the woods, dropping breadcrumbs every second as he walked so that he wouldn’t get lost. (Birds ate the crumbs, so he ended up getting lost and eaten by small rodents.) Anyway……….

17) What would the pattern of the breadcrumbs look like if the boy were walking at constant speed?18) If the crumbs seem to be spaced out at farther and farther intervals, what was the boy doing?19) If the crumbs seem to be spaced closer together, what was the boy doing?20) If there is a pile of breadcrumbs in one spot, what was the boy doing?

A ball is thrown straight upward.

21) What happens to the ball’s velocity while it is in the air?22) What happens to the ball’s speed while it is in the air?23) How fast is the ball going when it reaches its maximum height?24) What is the acceleration of the ball when it reaches its maximum height?25) What is the acceleration of the ball just before it hits the ground?

What can a graph of velocity vs. time tell you about…

26) …displacement? Explain.27) … acceleration? Explain.

A girl at the top of a building of height 1.10 x 102 m throws a water balloon downward onto the head of an unsuspecting rodent. It takes 4.00 s for the balloon to travel from the girl’s hand to the rodent’s skull.

28) At what velocity does the water balloon hit the rodent?

29) At what speed does the water balloon leave the girl’s hand?

An idiot shoots a gun straight up into the air on New Year’s Eve. The “muzzle velocity” of the gun (the speed at which the bullet leaves) is 3.00 x 102 m/s.

30) What is the velocity of the bullet 45.0 s after it leaves the gun?

31) What is the maximum altitude of the bullet?

A car is moving at 20.0 m/s [N] when it begins to constantly accelerate to a final velocity of 10.0 m/s [N]. It travels 1.50 x 102 m during this time.

32) How long did the acceleration last?

33) What was the average acceleration of the car during this time?

The next generation of deep-space probes may be powered by an “ion-drive” engine, which will provide a small but continuous acceleration for years at a time. (Rockets now provide large accelerations but only for a few minutes.) An ion-drive spacecraft leaves Earth orbit at 3.50 x 103 m/s and accelerates at 1.00 x 10-3 m/s2 for 1.50 x 1011 m (roughly the distance between the Earth and the sun).

34) What is its final speed at the end of that time?

35) How much time elapses as the spaceship accelerates?

On a mysterious planet in another solar system, an alien throws a rock upward, away from the planet. The rock leaves its tentacle at a height of 1.50 m above the ground with a speed of 5.00 m/s, and 20.0 s later lands on the ground.

36) What is the gravitational acceleration on this mysterious planet?

37) What is the velocity of the rock at the instant it strikes the ground?

Two-Dimensional Kinematics

The figure at right shows three situations in which identical projectiles are launched from the ground (at the same levels) at identical initial speeds and angles. The projectiles do not land on the same terrain, however.

38) Rank the situations according to the final speeds of the projectiles, greatest first.

39) Rank the situations according to the horizontal displacement of the projectiles, greatest first.

A projectile is launched from ground level with initial speed vo at an angle of 45° relative to the level ground, on which the projectile later lands.

40) If the launch angle were increased, would the range of the projectile increase, decrease, or remain the same?

41) If the launch angle were increased, would the flight time of the projectile increase, decrease, or remain the same?

An airplane flying horizontally at a constant speed of 350 km/hr over level ground releases a bundle of food supplies. Ignore air resistance.

42) What is the bundle’s initial vertical component of velocity?

43) What is the bundle’s initial horizontal component of velocity?

44) What is the bundle’s horizontal component of velocity just before hitting the ground?

45) If the airplane were instead moving at 450 km/hr, would the time of fall be larger, smaller, or the same?

We have been studying projectile motion while neglecting the effects of air resistance and the curvature of the earth. Consider what would happen if these factors were not ignored.

49) Does ignoring air resistance cause the final velocity of a projectile to overestimated or underestimated?

50) Does ignoring air resistance cause the maximum altitude of a projectile to overestimated or underestimated?

51) Does ignoring air resistance cause the time of flight of a projectile to overestimated or underestimated?

52) Does ignoring the curvature of the earth’s surface cause the final velocity of a projectile to overestimated or underestimated?

53) Does ignoring the curvature of the earth’s surface cause the maximum altitude of a projectile to overestimated or underestimated?

54) Does ignoring the curvature of the earth’s surface cause the time of flight of a projectile to overestimated or underestimated?

A

B

C

An accelerating airplane completes a 25.0 km [N10ºW] displacement as it accelerates at 3.00 m/s2 [W10ºN] over a period of 90 seconds. 55) What was its initial velocity?

56) What was its final velocity?

A man is initially running at 5.00 m/s [W10ºS]. Ten seconds later, he is running at 5.00 m/s [S10ºW].

57) What was his average acceleration during this time?

58) What was his displacement during this time?

A car is moving at 20.0 m/s [N] when it begins to constantly accelerate to a final velocity of 10.0 m/s [E]. The magnitude of its displacement during this time is 1.50 x 102 m.

59) How long did the acceleration last?

A basketball star is practicing his 3-point shooting. He releases the ball at time t = 0 at a point 2.25 m above the ground. The center of the basket is 3.05 meters above the ground and 7.0 meters north of the player. He shoots the ball so that it leaves his hand at 9.0 m/s.

60) If the player shoots the ball horizontally, how far away will it be when it hits the ground?

61) If the player shoots the ball in the direction [N35U], when will the ball hit the ground?

62) If the player shoots the ball in the direction [N35U], how far away will it be when it hits the ground?

63) If the player shoots the ball in the direction [N35U], what will be its maximum altitude (above the ground, not the starting point)?

64) In what direction should the player shoot the ball so that it passes through the center of the basket?

65) If the player shoots the ball in the direction [N35U], what will be its velocity just as it strikes the ground?

66) If the player shoots the ball in the direction [N35U], at what time(s) after the ball leaves his hand will it have a speed of 8.0 m/s?

A gun fires a projectile at an initial velocity of 105 m/s [E40ºU]. The gun is located 1.0 km from the western edge of a 50-m deep canyon. The canyon is 200-m wide, as shown at right.

67) When is the projectile moving in the direction [E20ºU]?

68) What is the horizontal displacement of the projectile when it has returned to ground level?

69) What is the horizontal displacement of the projectile if it strikes the bottom of the canyon?

70) What is the vertical displacement of the projectile if it strikes the east wall of the canyon?

71) What is the displacement of the projectile motion through the air?

72) What is the velocity of the projectile just before it strikes its actual impact point?

Circular Motion

A child is playing with a toy comprised of a massless 85-cm string attached to a small 0.04-kg ball. The child swings the ball in a vertical circle so that the period of the ball's rotation is 1.3 seconds.

73) What is the speed of the ball?

74) What is the acceleration of the ball?

A child is playing with a toy comprised of a massless 85-cm string attached to a small 0.04-kg ball. The child swings the ball in a horizontal circle so that the period of the ball's rotation is 1.3 seconds. The string makes an angle of 30° to the horizontal as the ball orbits the child’s hand.

75) What is the speed of the ball?

76) What is the acceleration of the ball?

A coin with a mass of 5 grams rests on a turntable at a spot 15 cm from the axis of rotation. The turntable rotates once per second, and the coin moves in a circular path without slipping.

75) What is the speed of the coin?

76) What is the acceleration of the coin?

A friendly Brazilian has a mass of 150 kg. Being in Brazil, he rotates in a circle around the center of the earth once per day. The radius of this circle (which is essentially the radius of the Earth) is 6.40 x 106 m.

77) What is the centripetal acceleration of the friendly Brazilian?3.38 x 10 -2 m/s2 [toward the center of the Earth]

FriendlyBrazilian

North Pole