Deck 3: Vectors in Physics

Question 1

Vector quantities are represented in terms of their magnitude and direction.

Answer 1

True

Question 2

Which of the following is a vector quantity?

A) time
B) mass
C) volume
D) displacement
E) speed

Answer 2

displacement

Question 3

A vector with zero magnitude can have one or more components that are nonzero.

Answer 3

False

Question 4

If + =0, then the vectors and have equal magnitudes and are directed in the same direction.

Question 5

Which of the following is a scalar quantity?

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

Question 6

If a vector has components A_x > 0, and A_y > 0, then the angle that this vector makes with the positive x-axis must be in the range

A) 0° to 90°.
B) 90° to 180°.
C) 180° to 270°.
D) 270° to 360°.
E) cannot be determined without additional information

Question 7

A student adds two displacement vectors that have the magnitudes of 12.0 m and 5.0 m. What is the range of possible answers for the magnitude of the resultant vector?

Question 8

If + = and A+B=C, then the vectors and are oriented perpendicular relative to one other.

Question 9

Which of the following statements is a true statement?

A) A vector can have positive or negative magnitudes.
B) A vector's magnitude cannot be more than the magnitude of one of its components.
C) A vector's magnitude cannot be less than the sum of the magnitude of its components.
D) If the x-component of a vector is smaller than its y-component then that vector is in the opposite direction to its y-component.
E) The magnitude of a vector cannot be zero unless all of its components are zero.

Question 10

If - =0, then the vectors and have equal magnitudes and are directed in the same direction.

Question 11

The magnitude of a unit vector is one.

Question 12

If a vector has components A_x < 0, and A_y < 0, then the angle that this vector makes with the positive x-axis must be in the range

A) 0° to 90°.
B) 90° to 180°.
C) 180° to 270°.
D) 270° to 360°.
E) cannot be determined without additional information

Question 13

If the magnitude of vector is less than the magnitude of vector , then the x-component of is less than the x-component of .

Question 14

If - = and A-B=C, then the vectors and are oriented perpendicular relative to one other.

Question 15

A scalar quantity multiplied by a unit vector is a scalar quantity.

Question 16

A car is moving with a constant speed along a circular track. The car is therefore not accelerating.

Question 17

Mass is a vector quantity.

Question 18

If the velocity vector of a car in a particular direction is increasing, the acceleration vector of that car in the same direction must also be increasing.

Question 19

If + = and A²+B²=C², then the vectors and are oriented perpendicular relative to one other.

Question 20

A component of a vector can be greater than the vector's magnitude.

Question 21

FIGURE 3-3
Refer to Figure 3-3. Three forces ₁ = ₂= ₃= 70 N are acting on an object O as shown in the figure. Which one of the following statements is true regarding the resultant force acting over the object O?

A) The resultant force is 35 N.
B) The resultant force is 70 N.
C) The resultant force is 140 N.
D) The resultant force is 210 N.
E) The resultant force is zero.

Question 22

Two vectors and are added together giving vector . The magnitude of C is such that C = . If the magnitudes of both vectors and are doubled, the magnitude of vector will

A) increase by a factor of 8.
B) increase by a factor of 4.
C) increase by a factor of 2.
D) increase by a factor of .
E) not change.

Question 23

If three vectors add up to a zero resultant it is correct to say that

A) it is impossible to find three vectors that add up to a zero resultant.
B) the three vectors must be co-linear.
C) the three vectors must be in a plane.
D) the three vectors must have the same magnitude.
E) the three vectors cannot have the same magnitude.

Question 24

The sum of two vectors has the greatest magnitude when the angle between these two vectors is

A) 90°.
B) 180°.
C) 60°.
D) 0°.
E) 270°.

Question 25

Vectors and satisfy the equation + = 0. These vectors satisfy one of the following statements.

A) Vectors and are at right angles to each other.
B) Vectors and point in the same direction.
C) The magnitude of is the negative of the magnitude of .
D) The magnitude of is twice the magnitude of .
E) Vectors and have the same lengths.

Question 26

Vector is obtained by rotating vector counterclockwise by 270°. The components of will

A) have the same signs as those of .
B) have opposite signs as those of .
C) The x-components will have opposite signs but the y-components will not.
D) The y-components will have opposite signs but the x-components will not.
E) depend on the quadrant where is.

Question 27

The resultant vector of two vectors and will have the minimum value when the angle between these vectors is one of the following?

A) 0°.
B) 90°.
C) 270°
D) 180°
E) 360°

Question 28

FIGURE 3-2
Refer to Figure 3-2. Vector as expressed in terms of vectors and is given by

A) + .
B) - .
C) .
D) .
E) None of the other choices is correct.

Question 29

Three vectors have equal magnitudes and make 120° with each other. We can say that

A) the magnitude of the resultant is one-third the magnitude of the component vectors.
B) the magnitude of the resultant is three times the magnitude of the component vectors.
C) the magnitude of the resultant is more than three times the magnitude of each component vector.
D) the resultant is zero.
E) the magnitude of the resultant is equal to the magnitude of the component vectors.

Question 30

A car travels along east and its velocity decreases. The acceleration of the car is in which of the following directions?

A) Eastward
B) Westward
C) Northward
D) Southward
E) Cannot be determined without additional information.

Question 31

The eastward component of vector is equal to the westward component of vector and their northward components are equal. Which one of the following statements is correct for these two vectors?

A) Vector is parallel to vector .
B) Vector is anti-parallel to vector .
C) Vector is perpendicular to vector .
D) Magnitude of vector is equal to the magnitude of vector .
E) Magnitude of vector is twice the magnitude of vector .

Question 32

Vector is initially pointing eastward. This vector is rotated clockwise by an angle of 110°. Which of the following statements is correct regarding the final position of vector ?

A) It is pointing 20° west of south.
B) It is pointing 70° south of east.
C) It is pointing 20° south of west.
D) It is pointing 70° east of south.
E) cannot be determined without additional information

Question 33

What is the angle between the vectors and - when these vectors are drawn from a common origin?

A) 90°
B) 0°
C) 360°
D) 180°
E) 270°

Question 34

FIGURE 3-2
Refer to Figure 3-2. Vector as expressed in terms of vectors and is given by

A) + .
B) - .
C) .
D) .
E) None of the other choices is correct.

Question 35

Vector has a magnitude of 16.0 m and is pointing eastward. Vector also has a magnitude of 16.0 m and is pointing westward. Vector is rotated clockwise by 110° and vector is rotated counterclockwise by 110°. Which one of the following statements is correct?

A) The northward component of vector is bigger than the northward component of vector .
B) The southward component of vector is bigger than the southward component of vector .
C) The eastward component of vector is bigger than the westward component of vector .
D) The westward component of vector is bigger than the eastward component of vector .
E) The westward component of vector is equal to the eastward component of vector .

Question 36

What is the smallest number of vectors that can be added to give a zero resultant?

A) 2
B) 3
C) 4
D) 5
E) You cannot add vectors and obtain a zero resultant.

Question 37

FIGURE 3-1
Refer to Figure 3-1. The components of vectors and are

A)
B)
C)
D)
E)

Question 38

A vector and an anti parallel vector when added together give a resultant vector that has a magnitude of 1.0 m. If vector has a magnitude of 7.0 m, which of the following is a possible magnitude of vector ?

A) 8.0 m
B) 7.0 m
C) 2.4 m
D) 6.9 m
E) 9.0 m

Question 39

When vectors and are added together they form vector and these vectors satisfy the relationship A² + B² = C². Which statement is true for these vectors?

A) Vectors and must be parallel.
B) Vectors and must be anti-parallel.
C) Vectors and must have the same magnitudes.
D) Vectors and must be perpendicular.
E) The magnitude of is the negative of the magnitude of .

Question 40

Vector is along the x-axis and vector is along the y-axis. Which one of the following statements is correct with respect to these vectors?

A) The x-component of vector is equal to the x-component of vector .
B) The y-component of vector is equal to the y-component of vector .
C) The x-component of vector is equal and opposite to the x-component of vector .
D) The y-component of vector is equal and opposite to the y-component of vector .
E) Vector does not have any component along the y-axis and vector does not have any component along the x-axis.

Question 41

You are trying to cross a river that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

A) due west.
B) due north.
C) due south.
D) in a southwesterly direction.
E) in a northwesterly direction.

Question 42

The components of vectors and are as follows: (1, -1) and (2, 4). The components of the resultant vector - are given by

A) (-1, -5).
B) (3, 3).
C) (1, -5).
D) (0, 4).
E) (-1,3)

Question 43

The components of vectors and are as follows: = (1, -1) and = (2, 4). The components of the resultant vector + are given by

A) (-1, 5).
B) (1, 5).
C) (0, 4).
D) (3, 3).
E) (1,-3)

Question 44

Vector has a magnitude of 16.0 m and is pointing eastward. It is rotated 110.0° clockwise. The component of this vector along west is

A) 15.0 m.
B) 5.47 m.
C) 18.7 m.
D) 12.4 m.
E) 44.0 m.

Question 45

A vector has components A_x = 12 m and A_y = 5.0 m. What is the magnitude of vector ?

A) 7.0 m
B) 13 m
C) 17 m
D) 60 m
E) 169 m

Question 46

Vector has a magnitude of 16.0 m and is pointing eastward. It is rotated counterclockwise by an angle of 110.0°. The component of this vector along west is

A) 5.47 m.
B) 15.0 m.
C) 18.7 m.
D) 12.4 m.
E) 44.0 m.

Question 47

Vector is 5.5 cm long and points along the x-axis. Vector is 7.5 cm long and points at +30° above the negative x-axis.
(a) Determine the x- and y-components of Vector .
(b) Determine the x- and y-components of Vector (c) Determine the sum of these two vectors in terms of components.
(d) Determine the sum of these two vectors in terms of magnitude and direction.

Question 48

A boat, whose speed in still water is 1.75 m/s, must aim upstream at an angle of 26.3° (with respect to a line perpendicular to the shore) in order to travel directly across the stream.
(a) Determine the speed of the current.
(b) Determine the resultant speed of the boat with respect to the shore.

Question 49

Vector = 4.00 m points eastward and vector = 3.00 m points southward. The resultant vector + is given by

A) 5.00 m at an angle 36.9° south of east.
B) 5.00 m at an angle 53.1° south of east.
C) 5.00 m at an angle 71.6° south of east.
D) 5.00 m at an angle 18.4° south of east.
E) 5.00 m at an angle 26.6° south of east.

Question 50

A car travels along eastward with a constant velocity. The magnitude of the acceleration of the car is

A) decreasing.
B) increasing.
C) non-zero constant.
D) zero.
E) None of the other choices is correct.

Question 51

Under which of the following conditions would a car have a westward acceleration?

A) As a car travels eastward with its velocity is increasing.
B) A a car travels eastward with its velocity is decreasing.
C) As a car travels westward with its velocity is decreasing.
D) As a car travels westward with its velocity is constant.
E) As a car travels eastward with its velocity is constant.

Question 52

If the acceleration of an object is always directed perpendicular to its velocity, then

A) the object is speeding up.
B) the object is slowing down.
C) the object is moving with a constant velocity.
D) the object is turning.
E) this situation would not be physically possible.

Question 53

If the acceleration vector of an object is directed parallel to the velocity vector, then

A) the object is speeding up.
B) the object is slowing down.
C) the object is moving with a constant velocity.
D) the object is turning.
E) the object is at rest.

Question 54

A boy jumps at a speed of 20.0 m/s at an angle of 25.0° above the horizontal. What is the horizontal component of the boy's velocity?

A) 18.1 m/s
B) 15.6 m/s
C) 8.45 m/s
D) 12.6 m/s
E) 9.33 m/s

Question 55

If the acceleration vector of an object is directed anti-parallel to the velocity vector, then

A) the object is speeding up.
B) the object is slowing down.
C) the object is moving with a constant velocity.
D) the object is turning.
E) the object is at rest.

Question 56

Vector = 4.00 m points eastward and vector = 3.00 m points northward. The resultant vector + is given by

A) 5.00 m at an angle 71.6° north of east.
B) 5.00 m at an angle 36.9° north of east.
C) 5.00 m at an angle 53.1° north of east.
D) 5.00 m at an angle 18.4° north of east.
E) 5.00 m at an angle 26.6° north of east.

Question 57

Vector = 4.0 m points eastward and vector = 3.0 m points westward. The resultant vector + is given by

A) 7.0 m east.
B) 7.0 m west.
C) 1.0 m east.
D) 1.0 m west.
E) 3.5 m west.

Question 58

A vector is located in the x-y plane. The x- and y-components of this vector are 4.00 m and 3.00 m, respectively. Find the angle that this vector makes with the positive y-axis.

A) 53.1°
B) 36.9°
C) 126.9°
D) 22.4°
E) 48.6°

Question 59

Vector is 75.0 cm long and points at 30° above the positive x-axis. Vector is 25.0 cm long and points along the negative x-axis. Vector is 40.0 cm long and points at 45° below the negative x-axis.
(a) Determine the x- and y-components of Vector .
(b) Determine the x- and y-components of Vector .
(c) Determine the x- and y-components of Vector .
(d) Determine the sum of these three vectors in terms of components.
(e) Determine the sum of these three vectors in terms of magnitude and direction.

Question 60

A vector has components A_x = 12.0 m and A_y= 5.00 m. What is the angle that vector makes with the x-axis?

A) 12.6°
B) 22.6°
C) 32.6°
D) 67.4°
E) 6.6°

Question 61

An airplane flies between two points on the ground that are 500 km apart. The destination is directly north of the origination of the flight. The plane flies with an air speed of 120 m/s. If a constant wind blows at 10.0 m/s due west during the flight, what direction must the plane fly relative to the air to arrive at the destination?

A) 4.78° east of north
B) 4.76° east of north
C) 85.2° west of north
D) 4.78° west of north
E) 4.76° west of north

Question 62

FIGURE 3-5
Refer to Figure 3-5. The sum of these vectors is given by

A) 4.0 cm along +x-axis.
B) 4.0 cm along -x-axis.
C) 4.0 cm along +y-axis.
D) 4.0 cm along -y-axis.
E) 4.0 cm 45° above +x-axis.

Question 63

A car moves from a point located 26.0 m from the origin and at an angle of 35.0° from the x-axis to a point located 56.0 m from the origin and at an angle of 60.0° from the x-axis in 2.50 s. What is the magnitude of the average velocity of the car?

A) 12.7 m/s
B) 13.7 m/s
C) 16.1 m/s
D) 18.3 m/s
E) 17.2 m/s

Question 64

FIGURE 3-4
Refer to Figure 3-4 The magnitudes of the forces as shown in the figure are:
F₁ = 80.0 N, F₂ = 60.0 N, and F₃ = 40.0 N. The resultant force acting on the particle O is given by

A) 180 N at an angle 60.0° with respect to +x-axis.
B) 60.0 N at an angle 90.0° with respect to +x-axis.
C) 20.0 N at an angle 34.3° with respect to +x-axis.
D) 35.5 N at an angle 34.3° with respect to +x-axis.
E) 40.0 N at an angle 60.0° with respect to +x-axis.

Question 65

Vector = 6.0 m and points 30° north of east. Vector = 4.0 m and points 30° south of west. The resultant vector + is given by

A) 2.0 m at an angle 30° north of east.
B) 2.0 m at an angle 60° north of east.
C) 10.0 m at an angle 60° east of north.
D) 10.0 m at an angle 30° north of east.
E) 10.0 m at an angle 60° north of east.

Question 66

A plane has an airspeed of 142 m/s. A 16.0 m/s wind is blowing southward at the same time as the plane is flying. If the velocity of the plane relative to Earth is due east, what is the magnitude of that velocity?

A) 16.2 m/s
B) 16.0 m/s
C) 158 m/s
D) 141 m/s
E) 48 m/s

Question 67

A plane has an airspeed of 142 m/s. A 30.0 m/s wind is blowing southward at the same time as the plane is flying. What must be the direction of the plane in order to move due east relative to the ground?

A) 78.1° north of east
B) 11.9° north of east
C) 77.8° north of east
D) 12.2° north of east
E) 55.3° north of east

Question 68

FIGURE 3-5
Refer to Figure 3-5. The components of the sum of these vectors are given by

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

Question 69

Vector = 8.0 m and points east, Vector = 6.0 m and points north, and vector = 5.0 m and points west. The resultant vector + + is given by

A) 2.0 m at an angle 63° north of east.
B) 2.0 m at an angle 63° east of north.
C) 6.7 m at an angle 63° east of north.
D) 6.7 m at an angle 63° north of east.
E) 3.8 m at an angle 67° north of east

Question 70

Vector = 6.0 m and points 30° south of east. Vector = 4.0 m and points 30° east of south. The resultant vector + is given by

A) 9.7 m at an angle 42° south of east.
B) 1.1 m at an angle 42° south of east.
C) 13.7 m at an angle 42° south of east.
D) 0.7 m at an angle 42° south of east.
E) 4.7 m at an angle 42° south of east.

Question 71

Vector = 6.0 m and points 30° east of south. Vector = 4.0 m and points 30° west of north. The resultant vector + is given by

A) 2.0 m at an angle 30° north of west.
B) 2.0 m at an angle 30° east of south.
C) 10.0 m at an angle 60° north of west.
D) 10.0 m at an angle 60° east of south.
E) 1.0 m at an angle 60° north of west

Question 72

Vector = 6.0 m and points 30° south of east. Vector = 4.0 m and points 30° south of west. The resultant vector + is given by

A) 3.3 m at an angle 71° south of east.
B) 5.3 m at an angle 71° south of east.
C) 3.3 m at an angle 19° south of east.
D) 5.3 m at an angle 19° south of east.
E) 2.6 m at an angle 19° south of east.

Question 73

Vector = 6.0 m and points 30° north of east. Vector = 4.0 m and points 30° west of south. The resultant vector + is given by

A) 2.7 m at an angle 8.3° south of east.
B) 2.7 m at an angle 8.3° east of south.
C) 3.2 m at an angle 8.3° east of south.
D) 3.2 m at an angle 8.3° south of east.
E) 2.3 m at an angle 8.3° south of east.

Question 74

Vector = 6.0 m and points 30° north of east. Vector = 4.0 m and points 30° west of north. The resultant vector + is given by

A) 9.8 m at an angle 64° east of north.
B) 9.8 m at an angle 26° north of east.
C) 7.2 m at an angle 26° east of north.
D) 3.3 m at an angle 26° north of east.
E) 3.3 m at an angle 64° east of north.

Question 75

Vector = 8.0 m and points 30° north of east, Vector = 6.0 m and points 30° west of north, and vector = 5.0 m and points 30° west of south. The resultant vector + + is given by

A) 2.7 m at an angle 74° north of east.
B) 5.9 m at an angle 74° north of east.
C) 4.8 m at an angle 74° east of north.
D) 5.1 m at an angle 74° north of east.
E) 2.1 m at an angle 66° east of north.

Question 76

Vector = 6.0 m and points 30° north of east. Vector = 4.0 m and points 30° east of north. The resultant vector + is given by

A) 0.7 m at an angle 42° north of east.
B) 13.7 m at an angle 42° north of east.
C) 1.1 m at an angle 42° north of east.
D) 9.7 m at an angle 42° north of east.
E) 2.0 m at an angle 42° north of east.

Question 77

Vector = 6.0 m and points 30° south of east. Vector = 4.0 m and points 30° west of south. The resultant vector + is given by

A) 7.2 m at an angle 64° south of east.
B) 3.3 m at an angle 64° south of east.
C) 9.8 m at an angle 26° south of east.
D) 9.8 m at an angle 64° south of east.
E) 3.3 m at an angle 26° south of east.

Question 78

Vector = 6.0 m and points 30° south of east. Vector = 4.0 m and points 30° north of west. The resultant vector + is given by

A) 10.0 m at an angle 30° south of east.
B) 10.0 m at an angle 60° east of south.
C) 2.0 m at an angle 60° south of east.
D) 2.0 m at an angle 30° south of east.
E) 1.0 m at an angle 30° east of south.

Question 79

Vector = 6.0 m and points 30° east of north. Vector = 4.0 m and points 30° west of south. The resultant vector + is given by

A) 10.0 m at an angle 60° north of east.
B) 10.0 m at an angle 30° east of north.
C) 2.0 m at an angle 30° north of east.
D) 2.0 m at an angle 60° north of east.
E) 1.0 m at an angle 60° east of north

Question 80

A plane is headed eastward at a speed of 156 m/s. A 20.0 m/s wind is blowing southward at the same time as the plane is flying. The velocity of the plane relative to the ground is

A) 157 m/s at an angle 7.31° south of east.
B) 157 m/s at an angle 7.31° east of south.
C) 155 m/s at an angle 7.36° south of east.
D) 155 m/s at an angle 7.36° east of south.
E) 157 m/s at an angle 7.36° south of east.