Deck 3: Motion in Two and Three Dimensions

Question 1

The components of a vector are A_x = -10 units and A_y = -6 units. What angle does this vector make with the positive x axis?

A) 31º
B) -31º
C) 180º - 31º
D) 180º + 31º
E) 90º - 31º

Answer 1

180º + 31º

Question 2

The angle between vectors and is 30º, and . Which vector diagram correctly describes the vectors , and ?

A) 1)
B) 2)
C) 3)
D) 4)
E) 5)

Answer 2

3)

Question 3

Vector has components A_x = +4.0 units and A_y = +3.2 units, whereas vector has components B_x = +2.5 units and B_y = +5.5 units. The angle between the two vectors is

A) 24º.
B) 65º.
C) 27º.
D) 39º.
E) 14º.

Answer 3

27º.

Question 4

The vector equation that describes the relationship among vectors , , and is

A) .
B) .
C) .
D) .
E) .

Question 5

Two vector quantities, whose directions can be altered at will, can have a resultant between the limits 5 and 15. The magnitudes of these two vector quantities could be

A) 2 and 2.
B) 5 and 10.
C) 20 and 40.
D) 20 and 50.
E) 59 and 97.

Question 6

Three vectors, , , and have the following x and y components: The magnitude of the resultant of , , and is

A) 3.3.
B) 5.0.
C) 11.
D) 7.8.
E) 14.

Question 7

Vectors , , and have the following components, expressed in arbitrary units: Vector is defined so that = 0 The magnitude and direction of relative to the positive x axis are

A) 7.6 units at -26º.
B) 7.6 units at 154º.
C) 14 units at 26º.
D) 3.5 units at 29º.
E) 10 units at 29º.

Question 8

What is the least number of non-zero vectors that can be added to give a resultant equal to zero?

A) 2
B) 3
C) 4
D) 5
E) It cannot be done.

Question 9

Which of the following vector equations correctly describes the relationship among the vectors shown in the figure below?

A)
B)
C)
D)
E) None of these equations are correct.

Question 10

The components of a vector are A_x = -10 units and A_y = 6 units. What angle does this vector make with the positive x axis?

A) 31º
B) -31º
C) 180º - 31º
D) 180º + 31º
E) 90º - 31º

Question 11

The vector in the figure below that could represent the vector is

A) .
B) .
C) .
D) .
E) .

Question 12

Vectors and have the following components: The angle between the negative x axis and the vector is

A) -45º.
B) 194º.
C) 37º.
D) -54º.
E) 86º.

Question 13

Vectors and have the following components: The angle between the positive x axis and the vector is

A) -45º.
B) 194º.
C) 37º.
D) -54º.
E) 86º.

Question 14

Three vectors, , , and have the following x and y components: The angle that the resultant makes with the positive direction of the x axis is

A) 1.2º.
B) 36º.
C) 50º.
D) 40º.
E) 70º.

Question 15

What is the least number of unequal non-zero vectors that can be added to give a resultant equal to zero?

A) 2
B) 3
C) 4
D) 5
E) It cannot be done.

Question 16

Two vectors and are added to give a resultant . The components of are A_x = -8.0 units and A_y = 6.0 units, and the components of are B_x = 1.0 units and B_y = -1.0 units. The magnitude of vector is

A) -1.0 units.
B) +8.6 units.
C) +19 units.
D) +2.0 units.
E) -3.2 units.

Question 17

Which of the following is NOT a vector?

A) velocity
B) acceleration
C) displacement
D) mass
E) force

Question 18

The vector in the figure below that could represent the vector is

A) .
B) .
C) .
D) .
E) .

Question 19

The angle between vectors and is 30º, and their sum is . Which vector diagram correctly describes the vectors , and ?

A) 1)
B) 2)
C) 3)
D) 4)
E) 5)

Question 20

Two vector quantities, whose directions can be altered at will, can have a resultant of any magnitude between the limits 0 and 200. The magnitude of each vector quantity must therefore be

A) between 0 and 80.
B) between 120 and 200.
C) less than 100.
D) exactly 100.
E) more than 100.

Question 21

A vector A is shown below. The x and y components of the vector are, respectively,

A) A sin $\alpha$ , A cos $\alpha$ ) or A sin $\theta$ , A cos $\theta$ ).
B) A sin $\alpha$ , A cos $\alpha$ ) or A cos $\theta$ , A sin $\theta$ ).
C) A sin $\alpha$ , A sin $\alpha$ ) or A sin $\theta$ , A cos $\theta$ ).
D) A cos $\alpha$ , A cos $\alpha$ ) or A sin $\theta$ , A cos $\theta$ ).
E) A cos $\alpha$ , A cos $\alpha$ ) or A cos $\theta$ , A cos $\theta$ ).

Question 22

The components of four vectors are as follows: The angle that the resultant vector makes with the positive x-axis is

A) -40º.
B) 59º.
C) -49.5º.
D) 37º.
E) -23º.

Question 23

The velocity vector of an object is given by and 4 s later, its velocity vector is . The units are in m/s. The average acceleration vector, in m/s² is

A) .
B) .
C) .
D) .
E) None of these is correct.

Question 24

You walk 5 km north and then 12 km east. Your resultant displacement is

A) 13 km at an angle of 22.6º north of east.
B) 13 km at an angle of 67.4º north of east.
C) 17 km at an angle of 22.6º north of east.
D) 17 km at an angle of 67.4º north of east.
E) None of these is correct.

Question 25

A velocity vector has an x component of +5.5 m/s and a y component of -3.5 m/s. The diagram that gives the direction of the vector is

A) 1).
B) 2).
C) 3).
D) 4).
E) None of these is correct.

Question 26

A velocity vector has an x component of -5.5 m/s and a y component of +3.5 m/s. The diagram that gives the direction of the vector is

A) 1).
B) 2).
C) 3).
D) 4).
E) None of these is correct.

Question 27

If an object is moving toward west, its acceleration

A) is directed towards north.
B) is directed towards east.
C) is directed towards west.
D) is directed towards south.
E) may be any direction.

Question 28

The velocity vector of an object is given by and 4 s later, its velocity vector is . The units are in m/s. The magnitude of the change in the velocity vector is

A) 1.4 m/s.
B) 2.8 m/s.
C) 5.7m/s.
D) 3.7 m/s.
E) 11.3 m.

Question 29

Vectors and have the following components: The magnitude of the vector is

A) 6.3 units.
B) 10.0 units.
C) 2.8 units.
D) 8.2 units.
E) 16 units.

Question 30

Three vectors and are added together. Which statement below best describes the additive property of the three vectors?

A)
B)
C)
D)
E) All of these

Question 31

The velocity vector of an object is given by and 4 s later, its velocity vector is . The units are in m/s. The angle that the change in the velocity vector makes with respect to the positive x-axis is given by

A) .
B) .
C) .
D) .
E) None of these is correct.

Question 32

Given vector , the vector

A) has a magnitude 3 times that of .
B) points in the same direction as .
C) has components each of which is 3 times those of .
D) makes the same angle with a given axis as does .
E) is described by all of these.

Question 33

A vector has an x component of 5.51 units and a y component of -9.52 units. The angle between the positive direction of the vector and the positive direction of the x-axis is approximately

A) 30^o.
B) -30^o.
C) 60^o.
D) -60^o.
E) None of these is correct.

Question 34

A particle has an initial velocity of 4.8 m/s toward the south and a final velocity of 7.1 m/s toward the east. The particle was subject to a constant acceleration for 0.25 s. The magnitude and the direction of the acceleration must have been

A) 2.3 m/s² at 34.1º north of east.
B) 8.6 m/s² at 34.1º north of east.
C) 34 m/s² at 34.1º north of east.
D) 34 m/s² at 34.1º south of east.
E) 8.6 m/s² at 34.1º south of east.

Question 35

The components of a vector

A) are not unique.
B) depend on the axes chosen.
C) can have one of the components equal to zero.
D) can be negative.
E) All are correct.

Question 36

Vectors , , , and have the following components: The magnitude of the resultant is

A) - 4.6 units.
B) 5.4 units.
C) 29 units.
D) 3.5 units.
E) 7.3 units.

Question 37

A vector of magnitude 5 points in the +y direction. Another vector of magnitude 4 is subtracted from the first vector. The smallest possible magnitude of the sum is

A) 1.
B) 4.
C) 5.
D) 9.
E) 10.

Question 38

What angle does the vector = +5, -12) make with the positive x-axis?

A) 67.4º
B) 22.6º
C) 36.9º
D) 53.1º
E) 292.6º

Question 39

A vector has an x component of -5.51 units and a y component of +9.52 units. The angle between the positive direction of the vector and the positive direction of the x-axis is

A) 125^o.
B) 60^o.
C) 120^o.
D) 150^o.
E) -60^o.

Question 40

A vector of magnitude 5 points in the +y direction. Another vector of magnitude 4 is added to the first vector. The largest possible magnitude of the sum is

A) 1.
B) 4.
C) 5.
D) 9.
E) 10.

Question 41

The position vector of an object is given by and 4 s later, its position vector is . The units are in m. The magnitude of the change in the position vector is

A) 0 m.
B) m.
C) m.
D) 10 m.
E) m.

Question 42

A car is traveling south at 30 km/h. It rounds a curve, and 6 s later it is traveling west at 30 km/h. The magnitude of the average acceleration of the car is

A) zero.
B) 60 km/h · s.
C) 5 km/h · s.
D) 50 km/h · s.
E) 7.1 km/h · s.

Question 43

The position vector of an object is given by and 4 s later, its position vector is . The units are in m. The angle that the change in the position vector makes with respect to the positive x-axis is given by

A) .
B) .
C) .
D) .
E) None of these is correct.

Question 44

The position vector of an object is given by and 4 s later, its position vector is . The units are in m. The average velocity vector, in m/s is

A) .
B) .
C) .
D) .
E) None of these is correct.

Question 45

The magnitude of the displacement of a particle is _______ the distance the particle has traveled.

A) larger than
B) smaller than
C) either larger or smaller than
D) the same as
E) smaller than or equal to

Question 46

The curve shows the position of an object with time. The object moves with a constant speed, v. Which of the vector diagrams below best represent the change in velocity vector from P₁ to P₂?

A) 1)
B) 2)
C) 3)
D) 4)
E) None of these is correct.

Question 47

A car is at position x₁, y₁) = 4 m, 5 m) at time t₁ = 1 s. If 10 seconds later the car moving in a straight line is at position x₂, y₂) = 204 m, 305 m), find the size of the) component of the average velocity along the x-axis.

A) 30.0 m/s
B) 36.1 m/s
C) 20.0 m/s
D) 18.2 m/s
E) 22.2 m/s

Question 48

The position vector of an object is given by and 4 s later, its position vector is . The units are in m. The change in the position vector , in m, is

A) .
B) .
C) .
D) .
E) None of these is correct.

Question 49

A particle initially moving at 4.0 m/s along the x-axis is uniformly accelerated at 3.0 m/s² along the y-axis for 2.0 s. The final speed of the particle is

A) -2.0 m/s.
B) 8.2 m/s.
C) 6.0 m/s.
D) 10 m/s.
E) None of these is correct.

Question 50

The distance traveled by a particle is _______ the magnitude of the displacement of the particle.

A) larger than or equal to
B) smaller than
C) either larger or smaller than
D) the same as
E) smaller than or equal to

Question 51

A car is at position x₁, y₁) = 4 m, 5 m) at time t₁ = 1 s. If 10 seconds later the car moving in a straight line is at position x₂, y₂) = 204 m, 305 m), calculate the distance traveled by the car in this interval.

A) 367 m
B) 500 m
C) 373 m
D) 509 m
E) 361 m

Question 52

The initial path of a rocket is 30° above the horizontal, and the horizontal component of the rocket's velocity is 326 m/s. The initial vertical component of the rocket's velocity is

A) 188 m/s.
B) 330 m/s.
C) 380 m/s.
D) 280 m/s.
E) 250 m/s.

Question 53

A car proceeding due south at 60 km/h ) makes a right turn, after which it is traveling due west at 80 km/h ). What is its change in velocity )?

A) 100 km/h 37º north of west
B) 100 km/h 37º south of west
C) 20 km/h west
D) 20 km/h 37º north of west
E) 20 km/h 37º south of west

Question 54

A particle initially moving at 4.0 m/s along the y-axis is uniformly accelerated at 3.0 m/s² along the x-axis for 2.0 s. The final speed of the particle is

A) -2.0 m/s.
B) 7.2 m/s.
C) 6.0 m/s.
D) 10 m/s.
E) None of these is correct.

Question 55

A car is at position x₁, y₁) = 4 m, 5 m) at time t₁ = 1 s. If 10 seconds later the car moving in a straight line is at position x₂, y₂) = 204 m, 305 m), calculate the magnitude of the average velocity during this interval.

A) 36.1 m/s
B) 32.8 m/s
C) 36.7 m/s
D) 50.0 m/s
E) 40.1 m/s

Question 56

A car is traveling east at 50 km/h. It rounds a curve, and 5 s later it is traveling north at 50 km/h. The magnitude of the average acceleration of the car is

A) zero.
B) 20 km/h · s.
C) 10 km/h · s.
D) 50 km/h · s.
E) None of these is correct.

Question 57

The curve shows the position of an object with time. The object moves with a constant speed, v. Which of the vector diagrams below best represent the change in position vector from P₁ to P₂?

A) 1)
B) 2)
C) 3)
D) 4)
E) None of these is correct.

Question 58

You walk 12 km south and then 5 km east. Your resultant displacement is

A) 13 km at an angle of 22.6º south of east.
B) 13 km at an angle of 67.4º south of east.
C) 17 km at an angle of 22.6º south of east.
D) 17 km at an angle of 67.4º south of east.
E) None of these is correct.

Question 59

A projectile is fired at an angle of 45° above the horizontal. If air resistance is neglected, the line in the graph that best represents the horizontal displacement of the projectile as a function of travel time is

A) 1.
B) 2.
C) 3.
D) 4.
E) None of these is correct.

Question 60

The curve shows the position of an object with time. The object moves with a constant speed, v. Which of the vector diagrams below best represent the velocity vector at P₁ and P₂?

A) 1)
B) 2)
C) 3)
D) 4)
E) None of these is correct.

Question 61

The figure represents the parabolic trajectory of a ball going from a to e in Earth gravity but without air resistance. The initial velocity of the ball is V_o at an angle $\theta$ to the horizon. The vertical dashed lines represent equal time interval, $\Delta$ t. The acceleration at point a is ____ the acceleration at c.

A) less than
B) equal to
C) greater than
D) Unable to tell.
E) Depends on how g changes along the path.

Question 62

Which of the following statements is not true of a projectile moving against negligible air resistance near the surface of Earth?

A) The horizontal velocity is constant.
B) The vertical acceleration is constant.
C) The horizontal displacement is directly proportional to the time of flight.
D) The vertical velocity at any given time is independent of the angle of projection.
E) The horizontal acceleration is constant.

Question 63

The maximum horizontal range of a rock that is thrown at the same speed but different angles with the horizon and that lands at a level, H, below the initial level occurs when the angle is

A) less than 0 $\degree$ .
B) 0 $\degree$ .
C) greater than 0 $\degree$ and less than 45 $\degree$ actual value depends on the value of H).
D) 45 $\degree$ ,
E) greater than 45 $\degree$ .

Question 64

The figure represents the parabolic trajectory of a ball going from A to E in Earth gravity but without air resistance. At point C the velocity of the ball is

A) a maximum and is directed to the right.
B) directed to the left.
C) a maximum.
D) a minimum and is directed to the right.
E) zero.

Question 65

The figure represents the parabolic trajectory of a ball going from a to e in Earth gravity but without air resistance. The initial velocity of the ball is V_o at an angle $\theta$ to the horizon. The vertical dashed lines represent equal time interval, $\Delta$ t. Consider "up" as the positive direction. The vertical velocity at point b is [Note: g = 9.81 m/s²)]

A) 0.
B) V_o cos $\theta$ ) - ½ g 2 $\Delta$ t)².
C) V_o sin $\theta$ ) - ½ g 2 $\Delta$ t)².
D) V_o sin $\theta$ ) + ½ g 2 $\Delta$ t)².
E) V_o cos $\theta$ ) + ½ g 2 $\Delta$ t)².

Question 66

A plane is flying horizontally at a height of 500 m and a constant speed of 429 km/h when an object is projected vertically downward at an initial speed of 35.0 m/s. If air resistance is neglected, the average vertical component of velocity between the object's release and its striking the ground is

A) 70.0 m/s.
B) 5.50 * 10³ m/s.
C) 140 m/s.
D) 105 m/s.
E) 35.0 m/s.

Question 67

The figure represents the parabolic trajectory of a ball going from a to e in Earth gravity but without air resistance. The initial velocity of the ball is V_o at an angle $\theta$ to the horizon. The vertical dashed lines represent equal time interval, $\Delta$ t. Consider UP as the positive direction. The vertical velocity at point c is [Note: g = 9.81 m/s²)]

A) V_o cos $\theta$ ).
B) V_o cos $\theta$ ) - ½ g 3 $\Delta$ t)².
C) V_o sin $\theta$ ) - ½ g 3 $\Delta$ t)².
D) 0.
E) V_o cos $\theta$ ) + ½ g 3 $\Delta$ t)².

Question 68

A projectile was fired at 35º above the horizontal. At the highest point in its trajectory its speed was 200 m/s. If air resistance is ignored, the initial velocity had a horizontal component of

A) zero.
B) 200 cos 35º) m/s.
C) 200 sin 35º) m/s.
D) 200/cos 35º) m/s.
E) 200 m/s.

Question 69

A projectile is fired horizontally from the top of a building in Earth gravity with an initial speed v₀. In the absence of air resistance, which of the graphs is representative of the projectile's motion?

A) 1)
B) 2)
C) 3)
D) 4)
E) 5)

Question 70

If a baseball is thrown at an angle of elevation of 30°, its range in the absence of air resistance is less than that of one thrown at

A) 0º.
B) 80º.
C) 20º.
D) 55º.
E) 90º.

Question 71

The figure represents the parabolic trajectory of a ball going from a to e in Earth gravity but without air resistance. The initial velocity of the ball is V_o at an angle $\theta$ to the horizon. The vertical dashed lines represent equal time interval, $\Delta$ t. The horizontal velocity at point c is

A) 0.
B) V_o cos $\theta$ ).
C) V_o sin $\theta$ ).
D) V_o.
E) depends on what g is along the path.

Question 72

If you ignore air resistance in projectile motion, the ________ of the projectile remains constant.

A) velocity vector
B) horizontal component of the velocity vector
C) vertical component of the velocity vector
D) speed
E) range

Question 73

A golfer drives her ball from the tee down the fairway in a high arcing shot. When the ball is at the highest point of its flight,

A) its velocity and acceleration are both zero.
B) its velocity is zero but its acceleration is nonzero.
C) its velocity is nonzero but its acceleration is zero.
D) its velocity and acceleration are both nonzero.
E) Insufficient information is given to answer correctly.

Question 74

A projectile is fired with an initial speed of 1000 m/s at an angle of 37° above the horizontal. If air resistance is neglected, the horizontal component of the projectile's velocity after 20 s is approximately

A) 600 m/s.
B) 800 m/s.
C) 640 m/s.
D) 40 m/s,
E) 160 m/s.

Question 75

A baseball is thrown with a velocity at an angle $\theta$ with the horizontal. The horizontal component of its velocity in the absence of air resistance is

A) v cos $\theta$
B) v cos $\theta$ - gt.
C) v² + 2gx.
D) v² - 2gx.
E) v sin $\theta$ - gt.

Question 76

The figure represents the parabolic trajectory of a ball going from A to E in Earth gravity but without air resistance. What is the direction of the acceleration at point C?

A) It is to the right.
B) It is to the left.
C) It is straight up.
D) It is straight down.
E) The acceleration of the ball is zero.

Question 77

You shoot an arrow in a high arc toward a target located some distance away. At the highest point in its flight, the arrow's

A) velocity and acceleration are both nonzero.
B) velocity is zero but its acceleration is nonzero.
C) velocity is nonzero but its acceleration is zero.
D) velocity and acceleration are both zero.
E) Insufficient information is given to answer correctly.

Question 78

A projectile is shot at an angle of 45º to the horizontal near the surface of Earth but in the absence of air resistance. When it reaches the highest point of its trajectory, its speed is 150 m/s. In a second trial with the same projectile, the initial speed is the same but the angle is now 37º with the horizontal. At its highest point in this trajectory, the speed of the projectile would be

A) 150 m/s sin 45º/sin 36º).
B) 150 m/s cos 37º/cos 45º).
C) 150 m/s sin 37º/sin 45º).
D) 150 m/s (37/45).
E) None of these is correct.

Question 79

The figure represents the parabolic trajectory of a ball going from A to E in Earth gravity but without air resistance. What is the direction of the acceleration at point B?

A) It is up and to the right.
B) It is down and to the left.
C) It is straight up.
D) It is straight down.
E) The acceleration of the ball is zero.

Question 80

A rescue airplane is diving at an angle of 37º below the horizontal with a speed of 250 m/s. It releases a survival package when it is at an altitude of 600 m. If air resistance is ignored, the horizontal distance of the point of impact from the plane at the moment of the package's release is

A) 2.80 * 10³ m.
B) 720 m.
C) 6.80 * 10³ m.
D) 420 m.
E) 5.50 * 10³ m.