Motion In Two And Three Dimensions Chapter 4 Test Bank

Chapter: Chapter 4

Learning Objectives:

LO 4.1.0 Solve problems related to position and displacement

LO 4.1.1 Draw the components of a 2D or 3D position vector of a particle, indicating the components.

LO 4.1.2 Determine the direction and magnitude of a position vector from its components, and vice versa.

LO 4.1.3 Apply the relationship between a particle’s displacement vector and its initial and final position vectors.

LO 4.2.0 Solve problems related to average velocity and instantaneous velocity

LO 4.2.1 Identify that velocity is a vector quantity and thus has both magnitude and direction and also has components.

LO 4.2.2 Draw the components of a 2D or 3D velocity vector of a particle, indicating the components.

LO 4.2.3 In magnitude-angle and unit-vector notations, relate a particle’s initial and final position vectors, the time interval between those positions, and the particle’s average velocity vector.

LO 4.2.4 Given a particle’s position vector as a function of time, determine its (instantaneous) velocity vector.

LO 4.3.0 Solve problems related to average acceleration and instantaneous acceleration

LO 4.3.1 Identify that acceleration is a vector quantity and thus has both magnitude and direction and also has components.

LO 4.3.2 Draw the components of a 2D or 3D acceleration vector of a particle, indicating the components.

LO 4.3.3 Given the initial and final velocity vectors of a particle and the time interval between those velocities, determine the average acceleration vector in magnitude-angle and unit-vector notations.

LO 4.3.4 Given a particle’s velocity vector as a function of time, determine its (instantaneous) acceleration vector.

LO 4.3.5 For each dimension of motion, apply the constant-acceleration equations (Chapter 2) to relate acceleration, velocity, position, and time.

LO 4.4.0 Solve problems related to projectile motion

LO 4.4.1 On a sketch of the path taken in projectile motion, explain the magnitudes and directions of the velocity and acceleration components during the flight.

LO 4.4.2 Given the launch velocity in either magnitude-angle or unit-vector notation, calculate the particle’s position, displacement, and velocity at a given instant during the flight.

LO 4.4.3 Given data for an instant during the flight, calculate the launch velocity.

LO 4.5.0 Solve problems related to uniform circular motion

LO 4.5.1 Sketch the path taken in uniform circular motion and explain the velocity and acceleration vectors (magnitude and direction) during the motion.

LO 4.5.2 Apply the relationships between the radius of the circular path, the period, the particle’s speed, and the particle’s acceleration magnitude.

LO 4.6.0 Solve problems related to relative motion in one dimension

LO 4.6.1 Apply the relationship between a particle’s position, velocity, and acceleration as measured from two reference frames that move relative to each other at constant velocity and along a single axis.

LO 4.7.0 Solve problems related to relative motion in two dimensions

LO 4.7.1 Apply the relationship between a particle’s position, velocity, and acceleration as measured from two reference frames that move relative to each other at constant velocity and in two dimensions.

Multiple Choice

1. Which of the following is a scalar quantity?

A) Speed

B) Velocity

C) Displacement

D) Acceleration

E) None of these

Difficulty: Easy

Section: 4-1

Learning Objective 4.1.1

2. Velocity is defined as:

A) rate of change of position with time

B) position divided by time

C) rate of change of acceleration with time

D) a speeding up or slowing down

E) change of position

Difficulty: Easy

Section: 4-2

Learning Objective 4.2.0

3. Which of the following is a vector quantity?

A) Mass

B) Density

C) Speed

D) Temperature

E) None of these

Difficulty: Easy

Section: 4-2

Learning Objective 4.2.0

4. Sally starts from home, walks 300 m east and then 500 m south, and arrives at her school. How far, in a straight line, is Sally’s school from her home?

A) 300 m

B) 500 m

C) 580 m

D) 640 m

E) 800 m

Difficulty: Easy

Section: 4-1

Learning Objective 4.1.2

5. From your window you can see a high-rise building several blocks away. You check the map and see that the building is 560 m away from you in a straight line, in a direction 30° south of east. However, the roads are all east-west and north-south. If you want to walk from your house to the building, how far in each direction do you have to walk?

A) 480 m east and 280 m south

B) 280 m east and 480 m south

C) 280 m east and 280 m south

D) 480 m east and 50 m south

E) cannot be determined without looking at the streets on the map

Difficulty: Easy

Section: 4-1

Learning Objective 4.1.2

6. A particle goes from x = –2 m, y = 3 m, z = 1 m to x = 3 m, y = –1 m, z = 4 m. Its displacement is:

A) (1 m) + (2 m) + (5 m)

B) (5 m) − (4 m) + (3 m)

C) −(5 m) + (4 m) − (3 m)

D) −(1 m) − (2 m) − (5 m)

E) −(5 m) − (2 m) − (3 m)

Difficulty: Easy

Section: 4-1

Learning Objective 4.1.3

7. A jet plane in straight horizontal flight passes over your head. When it is directly above you, the sound seems to come from a point behind the plane in a direction 30 from the vertical. The speed of the plane is:

A) the same as the speed of sound

B) half the speed of sound

C) three-fifths the speed of sound

D) 0.866 times the speed of sound

E) twice the speed of sound

Difficulty: Medium

Section: 4-2

Learning Objective 4.2.0

8. What is the difference between speed and velocity?

A) Speed is the magnitude of velocity; velocity is a vector and has both magnitude and direction.

B) There is no difference.

C) Speed is the rate at which something moves, while velocity is the direction in which it moves.

D) Speed is used when describing motion in one dimension, while velocity is used when describing motion in two dimensions.

E) Speed is the rate at which velocity changes.

Difficulty: Easy

Section: 4-2

Learning Objective: 4.2.1

9. An object moves from x = –2.1 m, y = 3.7 m, z = 1.4 m to x = 3.3 m, y = –1.1 m, z = 4.2 m in a time of 5.3 s. What is its average velocity?

A) (0.23 m/s) + (0.49 m/s) + (0.53 m/s)

B) (5.4 m/s) − (4.8 m/s) + (2.8 m/s)

C) (1.0 m/s) − (0.91 m/s) + (0.53 m/s)

D) (1.0 m/s) + (0.91 m/s) + (1.1 m/s)

E) −(1.0 m/s) + (0.91 m/s) + (0.53 m/s)

Difficulty: Easy

Section: 4-2

Learning Objective 4.2.3

10. An object moves from x = –2.1 m, y = 3.7 m to x = 3.3 m, y = –1.1 m in a time of 5.3 s. What is its average velocity?

A) 7.2 m/s, 32° below the positive x-axis

B) 2.5 m/s, 48° below the positive x-axis

C) 1.4 m/s, 42° below the positive x-axis

D) 4.9 m/s, 76° below the positive x-axis

E) 0.92 m/s, 14° below the positive x-axis

Difficulty: Medium

Section: 4-2

Learning Objective 4.2.3

11. The position of an object as a function of time is given in meters by x = (at + bt²) + (ct). What is its velocity as a function of time?

A) v = (a + b) + (c)

B) v = (a + 2b) + (c)

C) v = (a + 2bt) + (c)

D) v = b

E) v = 2b

Difficulty: Medium

Section: 4-2

Learning Objective 4.2.4

12. A plane traveling north at 200 m/s turns and then travels south at 200 m/s. The change in its velocity is:

A) 0 m/s

B) 200 m/s north

C) 200 m/s south

D) 400 m/s north

E) 400 m/s south

Difficulty: Easy

Section: 4-3

Learning Objective 4.3.0

13. Acceleration is defined as:

A) rate of change of position with time

B) speed divided by time

C) rate of change of velocity with time

D) a speeding up or slowing down

E) change of velocity

Difficulty: Easy

Section: 4-3

Learning Objective 4.3.0

14. Which of the following is NOT an example of accelerated motion?

A) Vertical component of projectile motion

B) Circular motion at constant speed

C) A swinging pendulum

D) Earth's motion about sun

E) Horizontal component of projectile motion

Difficulty: Easy

Section: 4-3

Learning Objective 4.3.1

15. An object has a velocity of (5.4 m/s) − (4.8 m/s). Over a period of 1.3 s, its velocity changes to (1.7 m/s) + (5.9 m/s). What is its acceleration?

A) −(3.7 m/s) + (11 m/s)

B) −(2.8 m/s) + (8.2 m/s)

C) (3.7 m/s) + (11 m/s)

D) (2.8 m/s) + (8.2 m/s)

E) −(2.8 m/s) + (1.1 m/s)

Difficulty: Medium

Section: 4-3

Learning Objective 4.3.3

16. The velocity of an object as a function of time is given by v = (12.5t − 7.2t²) + (4.3t³). What is its acceleration as a function of time?

A) a = (12.5 − 14.4t) + (12.9t²)

B) a = (−7.2) + (4.3t)

C) a = (5.3t) + (12.9t²)

D) a = (−7.2) + (8.6t)

E) a = (−14.4t) + (4.3t²)

Difficulty: Medium

Section: 4-3

Learning Objective: 4.3.4

17. An object is at rest at x = 0 m, y = 0 m. It accelerates at a rate of (−3.2 m/s²) + (8.6 m/s²). After accelerating for 4.7 seconds its coordinates are:

A) x = −15 m, y = 40 m

B) x = −35 m, y = 95 m

C) x = −24 m, y = 170 m

D) x = −70 m, y = 190 m

E) x = −48 m, y = 340 m

Difficulty: Easy

Section: 4-3

Learning Objective 4.3.5

18. Two bodies are falling with negligible air resistance, side by side, above a horizontal plane. If one of the bodies is given an additional horizontal acceleration during its descent, it:

A) strikes the plane at the same time as the other body

B) strike the plane earlier than the other body

C) has the vertical component of its velocity altered

D) has the vertical component of its acceleration altered

E) follows a straight line path along the resultant acceleration vector

Difficulty: Easy

Section: 4-4

Learning Objective 4.4.0

19. The velocity of a projectile equals its initial velocity added to:

A) a constant horizontal velocity

B) a constant vertical velocity

C) a constantly increasing horizontal velocity

D) a constantly increasing downward velocity

E) a constant velocity directed at the target

Difficulty: Medium

Section: 4-4

Learning Objective 4.4.0

20. Identical guns fire identical bullets horizontally at the same speed from the same height above level planes, one on the Earth and one on the Moon. Which of the following three statements is/are true?

I. The horizontal distance traveled by the bullet is greater for the Moon.

II. The flight time is less for the bullet on the Earth.

III. The velocities of the bullets at impact are the same.

A) III only

B) I and II only

C) I and III only

D) II and III only

E) I, II, III

Difficulty: Medium

Section: 4-4

Learning Objective 4.4.0

21. A stone is thrown horizontally and follows the path XYZ shown. The direction of the acceleration of the stone at point Y is:

A) 

B) 

C)

D)

E)

Difficulty: Easy

Section: 4-4

Learning Objective 4.4.1

22. Which of the curves on the graph below best represents the vertical component v_y versus t for a projectile fired at an angle of 45 above the horizontal?

A) OC

B) DE

C) AB

D) AE

E) AF

Difficulty: Easy

Section: 4-4

Learning Objective 4.4.1

23. A bullet shot horizontally from a gun:

A) strikes the ground much later than one dropped vertically from the same point at the same instant

B) never strikes the ground

C) strikes the ground at approximately the same time as one dropped vertically from the same point at the same instant

D) travels in a straight line

E) strikes the ground much sooner than one dropped from the same point at the same instant

Difficulty: Easy

Section: 4-4

Learning Objective 4.4.0

24. A bomber flying in level flight with constant velocity drops a bomb before it is over the target. Neglecting air resistance, which one of the following is NOT true?

A) The bomber is over the target when the bomb strikes

B) The acceleration of the bomb is constant

C) The horizontal velocity of the plane equals the vertical velocity of the bomb when it hits the target

D) The bomb travels in a curved path

E) The time of flight of the bomb is independent of the horizontal speed of the plane

Difficulty: Easy

Section: 4-4

Learning Objective 4.4.0

25. The airplane shown is in level flight at an altitude of 0.50 km and a speed of 150 km/h. At what distance d should it release a heavy bomb to hit the target X? Take g = 10 m/s².

A) 150 m

B) 295 m

C) 417 m

D) 1500 m

E) 15,000 m

Difficulty: Medium

Section: 4-4

Learning Objective 4.4.2

26. An object is shot from the back of a railroad flatcar moving at 40 km/h on a straight horizontal road. The launcher is aimed upward, perpendicular to the bed of the flatcar. The object falls:

A) in front of the flatcar

B) behind the flatcar

C) on the flatcar

D) either behind or in front of the flatcar, depending on the initial speed of the object

E) to the side of the flatcar

Difficulty: Easy

Section: 4-4

Learning Objective 4.4.2

27. A stone is thrown outward from the top of a 59.4-m high cliff with an upward velocity component of 19.5 m/s. How long is the stone in the air? Assume that it lands on the ground below the cliff, and that the ground below the cliff is flat.

A) 4.00 s

B) 5.00 s

C) 6.00 s

D) 7.00 s

E) 8.00 s

Difficulty: Medium

Section: 4-4

Learning Objective 4.4.0

28. A large cannon is fired from ground level over level ground at an angle of 30 above the horizontal. The muzzle speed is 980 m/s. Neglecting air resistance, the projectile will travel what horizontal distance before striking the ground?

A) 4.3 km

B) 8.5 km

C) 43 km

D) 85 km

E) 170 km

Difficulty: Medium

Section: 4-4

Learning Objective 4.4.2

29. A boy on the edge of a vertical cliff 20 m high throws a stone horizontally outwards with a speed of 20 m/s. It strikes the ground at what horizontal distance from the foot of the cliff? Use g = 10 m/s²

A) 10 m

B) 40 m

C) 50 m

D) 50 m

E) none of these

Difficulty: Medium

Section: 4-4

Learning Objective 4.4.2

30. A cannon fires a projectile as shown. The dashed line shows the trajectory in the absence of gravity; points MNOP correspond to the position of the projectile at one second intervals. If g = 10 m/s², the lengths X,Y,Z are:

A) 5 m, 10 m, 15 m

B) 5 m, 20 m, 45 m

C) 10 m, 40 m, 90 m

D) 10 m, 20 m, 30 m

E) 0.2 m, 0.8 m, 1.8 m

Difficulty: Medium

Section: 4-4

Learning Objective 4.4.2

31. A dart is thrown horizontally toward X at 20 m/s as shown. It hits Y 0.1 s later. The distance XY is:

A) 2 m

B) 1 m

C) 0.5 m

D) 0.1 m

E) 0.05 m

Difficulty: Medium

Section: 4-4

Learning Objective 4.4.2

32. A projectile is fired over level ground with an initial velocity that has a vertical component of 20 m/s and a horizontal component of 30 m/s. Using g = 10 m/s², the distance from launching to landing points is:

A) 40 m

B) 60 m

C) 80 m

D) 120 m

E) 180 m

Difficulty: Medium

Section: 4-4

Learning Objective 4.4.2

33. A stone thrown from the top of a tall building follows a path that is:

A) circular

B) made of two straight line segments

C) hyperbolic

D) parabolic

E) a straight line

Difficulty: Easy

Section: 4-4

Learning Objective 4.4.0

34. Two projectiles are in flight at the same time. The acceleration of one relative to the other:

A) is always 9.8 m/s²

B) can be as large as 19.6 m/s²

C) can be horizontal

D) is zero

E) none of these

Difficulty: Easy

Section: 4-4

Learning Objective 4.4.0

35. A ball is thrown horizontally from the top of a 20-m high hill. It strikes the ground at an angle of 45. With what speed was it thrown? Use g = 10 m/s².

A) 14 m/s

B) 20 m/s

C) 28 m/s

D) 32 m/s

E) 40 m/s

Difficulty: Hard

Section: 4-4

Learning Objective 4.4.3

36. An object, tied to a string, moves in a circle at constant speed on a horizontal surface as shown. The direction of the displacement of this object, as it travels from W to X is:

A) 

B) 

C) 

D)

E)

Difficulty: Easy

Section: 4-5

Learning Objective 4.5.1

37. A toy racing car moves with constant speed around the circle shown below. When it is at point A its coordinates are x = 0, y = 3m and its velocity is (6 m/s). When it is at point B its velocity and acceleration are:

A) −(6 m/s) and (12 m/s²), respectively

B) (6 m/s) and −(12 m/s²), respectively

C) (6 m/s) and (12 m/s²), respectively

D) (6 m/s) and (12 m/s²), respectively

E) (6 m/s) and 0 m/s², respectively

Difficulty: Easy

Section: 4-5

Learning Objective 4.5.1

38. A particle moves at constant speed in a circular path. The instantaneous velocity and instantaneous acceleration vectors are:

A) both tangent to the circular path

B) both perpendicular to the circular path

C) perpendicular to each other

D) opposite to each other

E) none of the above

Difficulty: Easy

Section: 4-5

Learning Objective 4.5.1

39. An airplane makes a gradual 90 turn while flying at a constant speed of 200 m/s. The process takes 20.0 seconds to complete. For this turn the magnitude of the average acceleration of the plane is:

A) 0 m/s²

B) 40 m/s²

C) 20 m/s²

D) 14 m/s²

E) 10 m/s²

Difficulty: Medium

Section: 4-5

Learning Objective 4.5.2

40. An airplane is flying north at 500 km/h. It makes a gradual 180 turn at constant speed, changing its direction of travel from north through east to south. The process takes 40 s. The average acceleration of the plane for this turn is:

A) 12.5 km/hs, north

B) 12.5 km/hs, east

C) 12.5 km/hs, south

D) 25 km/hs, north

E) 25 km/hs, south

Difficulty: Medium

Section: 4-5

Learning Objective 4.5.2

41. An object is moving on a circular path of radius  meters at a constant speed of 4.0 m/s. The time required for one revolution is:

A) 2/² s

B) ²/2 s

C) /2 s

D) ²/4 s

E) 2/ s

Difficulty: Easy

Section: 4-5

Learning Objective 4.5.2

42. A stone is tied to a string and whirled at constant speed in a horizontal circle. The speed is then doubled without changing the length of the string. Afterward the magnitude of the acceleration of the stone is:

A) the same

B) twice as great

C) four times as great

D) half as great

E) one-fourth as great

Difficulty: Easy

Section: 4-5

Learning Objective 4.5.2

43. Two objects are traveling around different circular orbits with constant speed. They both have the same acceleration but object A is traveling twice as fast as object B. The orbit radius for object A is _______ the orbit radius for object B.

A) one-fourth

B) one-half

C) the same as

D) twice

E) four times

Difficulty: Easy

Section: 4-5

Learning Objective 4.5.2

44. A stone is tied to a 0.50-m string and whirled at a constant speed of 4.0 m/s in a vertical circle. Its acceleration at the top of the circle is:

A) 9.8 m/s², up

B) 9.8 m/s², down

C) 8.0 m/s², down

D) 32 m/s², up

E) 32 m/s², down

Difficulty: Easy

Section: 4-5

Learning Objective 4.5.2

45. A stone is tied to a 0.50-m string and whirled at a constant speed of 4.0 m/s in a vertical circle. The acceleration at the bottom of the circle is:

A) 9.8 m/s², up

B) 9.8 m/s², down

C) 8.0 m/s², up

D) 32 m/s², up

E) 32 m/s², down

Difficulty: Easy

Section: 4-5

Learning Objective 4.5.2

46. A car rounds a 20-m radius curve at a speed of 10 m/s. The magnitude of its acceleration is:

A) 0 m/s²

B) 0.20 m/s²

C) 5.0 m/s²

D) 40 m/s²

E) 400 m/s²

Difficulty: Easy

Section: 4-5

Learning Objective 4.5.2

47. For a biological sample in a 1.0-m radius centrifuge to have a centripetal acceleration of 25g its speed must be:

A) 11 m/s

B) 16 m/s

C) 50 m/s

D) 122 m/s

E) 245 m/s

Difficulty: Easy

Section: 4-5

Learning Objective 4.5.2

48. A girl jogs around a horizontal circle with a constant speed. She travels one fourth of a revolution, a distance of 25 m along the circumference of the circle, in 5.0 s. The magnitude of her acceleration is:

A) 0.31 m/s²

B) 1.3 m/s²

C) 1.6 m/s²

D) 3.9 m/s²

E) 6.3 m/s²

Difficulty: Medium

Section: 4-5

Learning Objective 4.5.2

49. A stone is tied to the end of a string and is swung with constant speed around a horizontal circle with a radius of 1.5 m. If it makes two complete revolutions each second, its acceleration is:

A) 0.24 m/s²

B) 2.4 m/s²

C) 24 m/s²

D) 240 m/s²

E) 2400 m/s²

Difficulty: Medium

Section: 4-5

Learning Objective 4.5.2

50. A Ferris wheel with a radius of 8.0m makes 1 revolution every 10 s. When he is at the top, essentially a diameter above the ground, he releases a ball. How far from the point on the ground directly under the release point does the ball land?

A) 0 m

B) 1.0 m

C) 8.0 m

D) 9.1 m

E) 16 m

Difficulty: Hard

Section: 4-4, 4-5

Learning Objective 4.4.2

51. A boat is able to move through still water at 20 m/s. It makes a round trip to a town 3.0 km upstream. If the river flows at 5 m/s, the time required for this round trip is:

A) 120 s

B) 150 s

C) 200 s

D) 300 s

E) 320 s

Difficulty: Easy

Section: 4-6

Learning Objective 4.6.1

52. A motor boat can travel at 10 km/h in still water. A river flows at 5 km/h west. A boater wishes to cross from the south bank to a point directly opposite on the north bank. At what angle must the boat be headed?

A) 27 E of N

B) 30 E of N

C) 45 E of N

D) 60 E of N

E) depends on the width of the river

Difficulty: Medium

Section: 4-6

Learning Objective 4.6.1

53. A boy wishes to cross a river in the shortest possible time, without necessarily landing directly across from his starting point. He can row at 2 m/s in still water and the river is flowing at 1 m/s. At what angle  should he point the bow (front) of his boat?

A) 30

B) 45

C) 60

D) 63

E) 90

Difficulty: Medium

Section: 4-6

Learning Objective 4.6.1

54. A girl wishes to swim across a river to a point directly opposite as shown. She can swim at 2 m/s in still water and the river is flowing at 1 m/s. At what angle  with respect to the line joining the starting and finishing points should she swim?

A) 30

B) 45

C) 60

D) 63

E) 90

Difficulty: Medium

Section: 4-6

Learning Objective 4.6.1

55. A boat is traveling upstream at 14 mph with respect to a river that is flowing at 6 mph (with respect to the ground). A man runs directly across the boat, from one side to the other, at 6 mph (with respect to the boat). The speed of the man with respect to the ground is:

A) 10 mph

B) 14 mph

C) 18.5 mph

D) 21 mph

E) 26 mph

Difficulty: Medium

Section: 4-7

Learning Objective 4.7.1

56. A ferry boat is sailing at 12 km/h 30 W of N with respect to a river that is flowing at 6.0 km/h E. As observed from the shore, the ferry boat is sailing:

A) 30 E of N

B) due N

C) 30 W of N

D) 45 E of N

E) none of these

Difficulty: Medium

Section: 4-7

Learning Objective 4.7.1