Deck 3: Vectors and Coordinate Systems

Question 1

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

A) True
B) False

Answer 1

False

Question 2

The components of vector are = + 3.90 and = -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°

Answer 2

314°

Question 3

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

Answer 3

5.5 m/s

Question 4

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

Question 5

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 re in perpendicular directions.
E) The statement is always true.

Question 6

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

Question 7

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

A) True
B) False

Question 8

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 9

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 10

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 11

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 12

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

A) True
B) False

Question 13

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 14

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.

Question 15

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 16

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 17

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 18

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

A) True
B) False

Question 19

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 20

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 21

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 22

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 23

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 24

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 25

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 26

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 27

Vectors and are shown in the figure. What is ?

A) 31.8
B) -32.0 - 2.00
C) 1028
D) 34.0
E) -2.00 - 32.0

Question 28

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 29

As shown in the figure, three force vectors act on an object. The magnitudes of the forces as shown in the figure are = 80.0 N, = 60.0 N, and = 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 30

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 31

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 32

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 33

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