Resolving Vectors into Components

Question 1

The right-triangle figure shows a velocity vector of 25.0 m/s at 40.0° above the horizontal. Which value fills the ? for the horizontal component?

Accepted Answer

19.2 m/s

Answer

32.6 m/s

Answer

21.0 m/s

Answer

25.0 m/s

Question 2

A force vector is drawn at 80.0 N and 35.0° above the horizontal. In the component triangle, what is the vertical component?

Accepted Answer

45.9 N

Answer

97.7 N

Answer

56.0 N

Answer

80.0 N

Question 3

The figure shows a 120 m displacement at 60.0° north of east. Which value fills the ? for the east component?

Accepted Answer

60.0 m

Answer

240 m

Answer

120 m

Answer

208 m

Question 4

A velocity vector has magnitude 18.0 m/s and is 25.0° above the +x axis. What is its x component?

Accepted Answer

16.3 m/s

Answer

19.9 m/s

Answer

8.39 m/s

Answer

18.0 m/s

Question 5

The component diagram shows a 45.0 N force at 53.0° above the horizontal. What is the vertical component?

Accepted Answer

35.9 N

Answer

56.3 N

Answer

45.0 N

Answer

59.8 N

Question 6

A 75.0 m displacement is drawn 70.0° above the horizontal. Which value fills the ? for the horizontal component?

Accepted Answer

25.7 m

Answer

70.5 m

Answer

75.0 m

Answer

206 m

Question 7

The figure shows a projectile's velocity of 32.0 m/s directed 15.0° above the horizontal. What is the vertical component?

Accepted Answer

8.28 m/s

Answer

30.9 m/s

Answer

8.57 m/s

Answer

32.0 m/s

Question 8

A rope tension of 150 N is drawn 20.0° above the horizontal. Which value fills the ? for the horizontal component?

Accepted Answer

141 N

Answer

51.3 N

Answer

54.6 N

Answer

150 N

Question 9

Use the labeled grid vector. What are its components?

Accepted Answer

x = +6.0 m, y = +4.5 m

Answer

x = +4.0 m, y = +3.0 m

Answer

x = +4.5 m, y = +6.0 m

Answer

x = +7.5 m, y = 0 m

Question 10

Use the grid. What are the x and y components of the force F?

Accepted Answer

x = -4.0 N, y = +10.0 N

Answer

x = +4.0 N, y = +10.0 N

Answer

x = -2.0 N, y = +5.0 N

Answer

x = -10.0 N, y = +4.0 N

Question 11

The grid shows a velocity arrow with its scale labeled. What are the components?

Accepted Answer

x = +15 m/s, y = -9.0 m/s

Answer

x = +5.0 m/s, y = -3.0 m/s

Answer

x = -15 m/s, y = +9.0 m/s

Answer

x = +9.0 m/s, y = -15 m/s

Question 12

A displacement arrow is shown on the labeled grid. Which components match the arrow?

Accepted Answer

x = +2.5 m, y = +2.0 m

Answer

x = +5.0 m, y = +4.0 m

Answer

x = +2.0 m, y = +2.5 m

Answer

x = -2.5 m, y = -2.0 m

Question 13

A force arrow is drawn on a grid with its scale labeled. What are its components?

Accepted Answer

x = -12 N, y = -16 N

Answer

x = -3.0 N, y = -4.0 N

Answer

x = -16 N, y = -12 N

Answer

x = +12 N, y = +16 N

Question 14

The labeled grid shows a velocity vector. What are the components?

Accepted Answer

x = +6.0 m/s, y = -6.0 m/s

Answer

x = -6.0 m/s, y = +6.0 m/s

Answer

x = +3.0 m/s, y = -3.0 m/s

Answer

x = +8.5 m/s, y = 0 m/s

Question 15

The diagram shows perpendicular displacement components of 9.0 m east and 12.0 m north. What resultant matches them?

Accepted Answer

15.0 m at 53.1° north of east

Answer

15.0 m at 36.9° north of east

Answer

21.0 m at 53.1° north of east

Answer

3.0 m at 45.0° north of east

Question 16

The figure gives force components of 24 N east and 7 N north. What are the magnitude and direction of the resultant force?

Accepted Answer

25 N at 16.3° north of east

Answer

25 N at 73.7° north of east

Answer

31 N at 16.3° north of east

Answer

17 N at 45.0° north of east

Question 17

A component diagram shows 5.0 m/s east and 12.0 m/s south. Which resultant velocity is correct?

Accepted Answer

13.0 m/s at 67.4° south of east

Answer

13.0 m/s at 22.6° south of east

Answer

17.0 m/s at 67.4° south of east

Answer

7.0 m/s at 45.0° south of east

Question 18

The diagram shows force components of 8.0 N west and 15.0 N north. What resultant force do they make?

Accepted Answer

17.0 N at 61.9° north of west

Answer

17.0 N at 28.1° north of west

Answer

23.0 N at 61.9° north of west

Answer

7.0 N at 45.0° north of west

Question 19

A runner's displacement is 50.0 m at 30.0° north of east. Taking +x east and +y north, what are the components?

Accepted Answer

x = +43.3 m, y = +25.0 m

Answer

x = +25.0 m, y = +43.3 m

Answer

x = +50.0 m, y = +25.0 m

Answer

x = +28.9 m, y = +50.0 m

Question 20

A velocity vector of 22.0 m/s points 120° counterclockwise from the +x axis. What are its x and y components?

Accepted Answer

x = -11.0 m/s, y = +19.1 m/s

Answer

x = +11.0 m/s, y = +19.1 m/s

Answer

x = -19.1 m/s, y = +11.0 m/s

Answer

x = +19.1 m/s, y = -11.0 m/s

Question 21

A 90.0 N force acts 40.0° below the +x axis. What are the force components?

Accepted Answer

x = +68.9 N, y = -57.9 N

Answer

x = +57.9 N, y = -68.9 N

Answer

x = +68.9 N, y = +57.9 N

Answer

x = +90.0 N, y = -57.9 N

Question 22

A cart has velocity 14.0 m/s at 210° measured counterclockwise from the +x axis. What are its components?

Accepted Answer

x = -12.1 m/s, y = -7.00 m/s

Answer

x = +12.1 m/s, y = +7.00 m/s

Answer

x = -7.00 m/s, y = -12.1 m/s

Answer

x = +7.00 m/s, y = -12.1 m/s

Question 23

A hiker's displacement is 125 m at 55.0° north of west. Taking +x east and +y north, what are the components?

Accepted Answer

x = -71.7 m, y = +102 m

Answer

x = -102 m, y = +71.7 m

Answer

x = +71.7 m, y = +102 m

Answer

x = -71.7 m, y = -102 m

Question 24

An acceleration vector has magnitude 3.20 m/s² at 75.0° above the +x axis. What are its components?

Accepted Answer

x = +0.828 m/s², y = +3.09 m/s²

Answer

x = +3.09 m/s², y = +0.828 m/s²

Answer

x = +3.20 m/s², y = +0.828 m/s²

Answer

x = +0.858 m/s², y = +3.20 m/s²

Question 25

A cable pulls with 240 N at 25.0° east of south. Taking +x east and +y north, what are the components?

Accepted Answer

x = +101 N, y = -218 N

Answer

x = +218 N, y = -101 N

Answer

x = -101 N, y = -218 N

Answer

x = +101 N, y = +218 N

Question 26

For a vector of magnitude A measured at angle θ counterclockwise from the +x axis, which component equations are correct?

Accepted Answer

Ax = A and Ay = A

Answer

Ax = A/ and Ay = A/

Question 27

A ball is launched with the same speed each time, but the angle above the horizontal is raised from 10° to 70°. What happens to the components?

Accepted Answer

The horizontal component decreases while the vertical component increases.

Answer

The horizontal component increases while the vertical component decreases.

Answer

Both components stay the same because the speed is unchanged.

Answer

Both components decrease because the angle is larger.

Question 28

Which quantity can be resolved into east and north components?

Accepted Answer

A displacement of 40 m at 30° north of east

Answer

A distance of 40 m

Answer

A speed of 40 m/s

Answer

A time interval of 40 s

Question 29

A support cable has tension T and makes an angle φ with the vertical wall, not with the horizontal floor. Which component statement is correct?

Accepted Answer

Horizontal component = T sin φ; vertical component = T cos φ

Answer

Horizontal component = T cos φ; vertical component = T sin φ

Answer

Horizontal component = T tan φ; vertical component = T sin φ

Answer

Horizontal component = T; vertical component = T cos φ

Question 30

Two displacement vectors are added by components. After adding all x parts and all y parts separately, what should you do to find the resultant?

Accepted Answer

Use R = √(Rx² + Ry²) and θ = tan⁻¹(Ry/Rx), with the quadrant checked.

Answer

Add the magnitudes of the original vectors and ignore direction.

Answer

Use R = Rx + Ry because components are scalar numbers.

Answer

Subtract the y component from the x component to get the magnitude.

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Resolving Vectors into Components

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Resolving Vectors into Components

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner