Deck 2: Motion Along a Straight Line

Question 1

Addition and subtraction: For the vectors shown in the figure, express vector in terms of vectors and .

Answer 1

= -

Question 2

Components: Which of the following is an accurate statement?

A) The magnitude of a vector can be zero even though one of its components is not zero.
B) It is possible to add a scalar quantity to a vector.
C) Even though two vectors have unequal magnitudes, it is possible that their vector sum is zero.
D) Rotating a vector about an axis passing through the tip of the vector does not change the vector.
E) The magnitude of a vector is independent of the coordinate system used.

Answer 2

The magnitude of a vector is independent of the coordinate system used.

Question 3

Addition and subtraction: A rabbit trying to escape a fox runs north for 8.0 m, darts northwest for 1.0 m, then drops 1.0 m down a hole into its burrow. What is the magnitude of the net displacement of the rabbit?

A) 8.8 m
B) 8.1 m
C) 66 m
D) 10 m

Answer 3

8.8 m

Question 4

Vector (cross) product: If two vectors are perpendicular to each other, their cross product must be zero.

Question 5

Scalar (dot) product: The value of the dot product of two vectors depends on the particular coordinate system being used.

Question 6

Unit vectors: If all the components of a vector are equal to 1, then that vector is a unit vector.

Question 7

Addition and subtraction: You walk to the north, then turn 60° to your right and walk another How far are you from where you originally started?

A) 87 m
B) 50 m
C) 94 m
D) 46 m

Question 8

Addition and subtraction: Under what condition is | - | = A + B?

A) The magnitude of vector is zero.
B) Vectors and
are in opposite directions.
C) Vectors and
are in the same direction.
D) Vectors and
are in perpendicular directions.
E) The statement is never true.

Question 9

Vector (cross) product: If and are nonzero vectors for which ∙ = 0, it must follow that

A) ×
= 0.
B) is parallel to
.
C) | ×
| = AB.
D) | ×
| = 1.

Question 10

Components: If the magnitude of vector is less than the magnitude of vector , then the x component of is always less than the x component of .

Question 11

Vector (cross) product: If two vectors point in opposite directions, their cross product must be zero.

Question 12

Scalar (dot) product: If two nonzero vectors point in the same direction, their dot product must be zero.

Question 13

Addition and subtraction: If - = 0, then the vectors and have equal magnitudes and are directed in the opposite directions from each other.

Question 14

Addition and subtraction: Vectors and are shown in the figure. Vector is given by = - . The magnitude of vector is 16.0 units, and the magnitude of vector is 7.00 units. What is the angle of vector , measured counterclockwise from the +x-axis?

A) 16.9°
B) 22.4°
C) 73.1°
D) 287°
E) 292°

Question 15

Scalar (dot) product: If the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other.

Question 16

Addition and subtraction: You walk 53 m to the north, then turn 60° to your right and walk another Determine the direction of your displacement vector. Express your answer as an angle relative to east.

A) 63° N of E
B) 50° N of E
C) 57° N of E
D) 69° N of E

Question 17

Addition and subtraction: Vectors and are shown in the figure. Vector is given by = - . The magnitude of vector is 16.0 units, and the magnitude of vector is 7.00 units. What is the magnitude of vector ?

A) 9.00
B) 9.53
C) 15.5
D) 16.2
E) 17.5

Question 18

Addition and subtraction: If A > B, under what condition is | - | = A - B?

A) The statement is never true.
B) Vectors and
are in opposite directions.
C) Vectors and
are in the same direction.
D) Vectors and
are in perpendicular directions.
E) The statement is always true.

Question 19

Components: The magnitude of a vector can never be less than the magnitude of one of its components.

Question 20

Components: If 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 about these two vectors is correct?

A) Vector is parallel to vector
.
B) Vectors and
point in opposite directions.
C) Vector is perpendicular to vector
.
D) The magnitude of vector is equal to the magnitude of vector
.
E) The magnitude of vector is twice the magnitude of vector
.

Question 21

Components: An airplane undergoes the following displacements: First, it flies 66 km in a direction 30° east of north. Next, it flies 49 km due south. Finally, it flies 100 km 30° north of west. Using vector components, determine how far the airplane ends up from its starting point.

A) 79 km
B) 81 km
C) 82 km
D) 78 km
E) 76 km

Question 22

Components: In the figure, the magnitude of vector is 18.0 units, and the magnitude of vector is 12.0 units. What vector must be added to the vectors and so that the resultant of these three vectors points in the -x direction and has a magnitude of 7.50 units? Use vector components to find your answer, and express vector by giving its magnitude and the angle it makes with the +x-axis taking counterclockwise to be positive.

Question 23

Components: The components of vector are A_x = + 3.90 and A_y = -4.00. What is the angle measured counterclockwise from the +x-axis to vector ?

A) 314°
B) 134°
C) 224°
D) 136°
E) 46.0°

Question 24

Components: Vector has a magnitude of 75.0 cm and points at 30° above the positive x-axis. Vector has a magnitude of 25.0 cm and points along the negative x-axis. Vector has a magnitude of 40.0 cm 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 x and y components of the sum of these three vectors.
(e) Determine the magnitude and direction of the sum of these three vectors.

Question 25

Components: A helicopter is flying horizontally with a speed of 444 m/s over a hill that slopes upward with a 2% grade (that is, the "rise" is 2% of the "run"). What is the component of the helicopter's velocity perpendicular to the sloping surface of the hill?

A) 8.9 m/s
B) 220 m/s
C) 435 m/s
D) 444 m/s

Question 26

Unit vectors: Vectors and are shown in the figure. What is |-5.00 + 4.00 |

A) 31.8
B) -32.0 - 2.00

C) 1028
D) 34.0
E) -2.00 - 32.0

Question 27

Scalar (dot) product: Determine the scalar product of = 6.0 + 4.0 - 2.0 and = 5.0 - 6.0 - 3.0 .

A) 30 + 24
+ 6

B) 30 - 24
+ 6

C) 12
D) 60
E) undefined

Question 28

Components: As shown in the figure, three force vectors act on an object. The magnitudes of the forces as shown in the figure are F₁ = 80.0 N, F₂ = 60.0 N, and F₃ = 40.0 N, where N is the standard SI unit of force. The resultant force acting on the object 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 29

Unit vectors: Vector = 1.00 + -2.00 and vector = 3.00 + 4.00 What are the magnitude and direction of vector = + ?

A) 7.21 in a direction 33.7° counterclockwise from the positive x axis
B) 6.00 in a direction 63.4° counterclockwise from the positive x axis
C) 4.47 in a direction 6.34° counterclockwise from the positive x axis
D) 4.47 in a direction 26.6° counterclockwise from the positive x axis
E) 7.21 in a direction 56.3° counterclockwise from the positive x axis

Question 30

Components: The components of vector are = + 2.2 and = -6.9 , and the components of vector are given are = -6.1 and = -2.2. What is the magnitude of the vector - ?

A) 9.5
B) 6.1
C) 9.9
D) 91
E) 0.76

Question 31

Components: An apple falls from an apple tree growing on a 20° slope. The apple hits the ground with an impact velocity of 16.2 m/s straight downward. What is the component of the apple's impact velocity parallel to the surface of the slope?

A) 5.5 m/s
B) 8.7 m/s
C) 12 m/s
D) 15 m/s

Question 32

Components: The components of vector are = -3.5 and = -9.7, and the components of vector are = -6 and = + 8.1. What is the angle (less than 180 degrees) between vectors and ?

A) 124°
B) 56°
C) 17°
D) 163°
E) 106°

Question 33

Unit vectors: If = + 4 - 2 - 3 and = - 4 -2 - 3 , which of the following numbers is closest to the magnitude of - ?

A) 8
B) 7
C) 9
D) 10
E) 11

Question 34

Unit vectors: Vector = -1.00 + -2.00 and vector = 3.00 + 4.00 What are the magnitude and direction of vector = 3.00 + 2.00 ?

A) 3.61 in a direction -56.3° counterclockwise from the positive x-axis
B) 3.61 in a direction 56.3° counterclockwise from the positive x-axis
C) 3.61 in a direction 33.7° counterclockwise from the positive x-axis
D) 5.00 in a direction 56.3° counterclockwise from the positive x axis
E) 6.72 in a direction 34.4° counterclockwise from the positive x-axis

Question 35

Components: Vector has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis. What are the x and y components of vector .

A) A_x = 3.83 and A_y = 3.21
B) A_x = 3.83 and A_y = -3.21
C) A_x = -3.21 and A_y = -3.83
D) A_x = -3.21 and A_y = 3.83
E) A_x = 4.29 and A_y = 2.16

Question 36

Components: Three forces are exerted on an object placed on a tilted floor. Forces are vectors. The three forces are directed as shown in the figure. If the forces have magnitudes = 1.0 N, = 8.0 N and = 7.0 N, where N is the standard unit of force, what is the component of the net force _net =
₁ +
₂ +
₃ parallel to the floor?

A) 2.5 N
B) 5.1 N
C) 6.0 N
D) 7.8 N

Question 37

Unit vectors: Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 . What is vector = + ?

A) 0.00 + 3.00

B) 7.00 + 7.00

C) -3.00 + 7.00

D) 0.00 + 7.00

E) -3.00 -3.00

Question 38

Components: A teacher sends her students on a treasure hunt. She gives the following instructions: 1. Walk 300 m north
2) Walk 400 m northwest
3) Walk 700 m east-southeast and the treasure is buried there.
As all the other students walk off following the instructions, Jane physics student quickly adds the displacements and walks in a straight line to find the treasure. How far and in what direction does Jane need to walk?

A) 187 m in a direction 67.3° north of east
B) 481 m in a direction 40.9° north of east
C) 399 m in a direction 52.5° north of east
D) 284 m in a direction 28.2° west of north
E) The treasure position cannot be reached in one straight walk.

Question 39

Unit vectors: What is the magnitude of + + , where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 and = -1.00 + 1.00 ?

A) 7.07
B) 2.00
C) 10.76
D) 6.78
E) 8.12

Question 40

Components: Vector has a magnitude of 5.5 cm and points along the x-axis. Vector has a magnitude of 7.5 cm 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 x and y components of the sum of these two vectors.
(d) Determine the magnitude and direction of the sum of these two vectors.

Question 41

Vector (cross) product: If the magnitude of the cross product of two vectors is one-half the dot product of the same vectors, what is the angle between the two vectors?

Question 42

Scalar (dot) product: The scalar product of vector = 3.00 + 2.00 and vector is 10.0. Which of the following vectors could be vector ?

A) 2.00 + 4.00

B) 4.00 + 6.00

C) 5.00 + 4.00

D) 12.0
E) 2.00 + 2.00

Question 43

Scalar (dot) product: If = 3 - + 4 and = x + - 5 , find x so will be perpendicular to .

Question 44

Vector (cross) product: What is the vector product of = 2.00 + 3.00 + 1.00 and = 1.00 - 3.00 - 2.00 ?

A) -3.00 + 5.00
- 9.00

B) -5.00 + 2.00
- 6.00

C) -9.00 - 3.00
- 3.00

D) -4.00 + 3.00
- 1.00

E) 2.00 - 9.00
- 2.00

Question 45

Vector (cross) product: For the vectors shown in the figure, find the magnitude and direction of the vector product × that the quantities shown are accurate to two significant figures.

A) 16, directed into the plane
B) 16, directed out of the plane
C) 45, directed on the plane
D) 45, directed into the plane
E) 45, directed out of the plane

Question 46

Vector (cross) product: If = -2 - 6 + 2 and = - 2 -2 - 3 , which of the following numbers is closest to the magnitude of × ?

A) 25
B) 21
C) 17
D) 13
E) 9

Question 47

Scalar (dot) product: What is the angle between the vector = + 3 - 2 - 3 and the +y-axis?

A) 115°
B) 65°
C) 25°
D) 155°
E) 90°

Question 48

Scalar (dot) product: The angle between vector = 2.00 + 3.00 and vector is The scalar product of vectors and is 3.00. If the x component of vector is positive, what is vector .

A)
B)
C)
D)
E)

Question 49

Scalar (dot) product: For the vectors shown in the figure, assume numbers are accurate to two significant figures. The scalar product × is closest to

A) zero.
B) 16.
C) 45.
D) -16.
E) -45.

Question 50

Scalar (dot) product: Determine the angle between the directions of vector = 3.00 + 1.00 and vector = -3.00 + 3.00 .

A) 26.6°
B) 30.0°
C) 88.1°
D) 117°
E) 45.2°

Question 51

Vector (cross) product: If = - 4 - 2 - 3 , what is × ?

A) +3 - 4

B) +3 + 4

C) -3 + 4

D) +3 + 2
- 4

E) -3 - 2
+ 4

Question 52

Vector (cross) product: What is the magnitude of the cross product of a vector of magnitude 2.00 m pointing east and a vector of magnitude 4.00 m pointing 30.0° west of north?

A) 6.93
B) -6.93
C) 4.00
D) -4.00
E) 8.00

Question 53

Scalar (dot) product: Two boys searching for buried treasure are standing underneath the same tree. One boy walks east and then north. The other boy walks west and then north. Find the scalar product of their net displacements from the tree.

Question 54

Scalar (dot) product: A rectangular box is positioned with its vertices at the following points: A = (0,0,0) C = (2,4,0) E = (0,0,3) G = (2,4,3)
B = (2,0,0) D = (0,4,0) F = (2,0,3) H = (0,4,3)
If the coordinates all have three significant figures, the angle between the line segments AG and AH is closest to:

A) 21.8°.
B) 22.5°.
C) 26.6°.
D) 36.9°.
E) 45.0°.

Question 55

Vector (cross) product: For the vectors shown in the figure, find the magnitude and direction of × , assuming that the quantities shown are accurate to two significant figures.

A) 26, directed into the plane
B) 26, directed out of the plane
C) 31, directed on the plane
D) 31, directed into the plane
E) 31, directed out of the plane