Practice Vectors in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

Mathematical quantities that possess both a magnitude (size) and a direction, represented graphically as arrows.

An arrow pointing somewhere with a certain length—the length is 'how much,' the direction is 'which way.'

Showing a random 20 of 50 problems.

Example 1

medium

Add vectors

6

N east and

8

N north. Find magnitude and confirm the triple.

Add 6 N east and 8 N north; find the resultant magnitude

Example 2

easy

A vector has components

v_x = -6

and

v_y = 8

. Find its magnitude.

Find the magnitude of vector v with components vx

Example 3

medium

Subtract:

\vec{A} - \vec{B}

where

\vec{A} = (7, 2)

and

\vec{B} = (3, 5)

Example 4

easy

Find the magnitude and direction of the vector with components

v_x = 3

and

v_y = 4

Resolve into components; find the resultant magnitude and angle θ

Example 5

easy

Add two collinear vectors:

8

N east and

3

N east.

Example 6

medium

Two equal vectors of magnitude

5

act at

90°

to each other. Find the resultant magnitude.

Find the resultant magnitude of two equal 5 N forces at 90° to each other

Example 7

easy

50

km/h a vector or a scalar?

Example 8

challenge

Three forces in equilibrium have magnitudes

5 \text{ N}

12 \text{ N}

, and

13 \text{ N}

. What is the angle between the

5 \text{ N}

and

12 \text{ N}

forces?

Example 9

easy

A vector has

v_x = 0

and

v_y = -7

. State its magnitude and direction.

State the magnitude and direction of the vector with vx

Example 10

hard

Find the dot product

\vec{A} \cdot \vec{B}

for

\vec{A} = (3, 2)

and

\vec{B} = (-4, 6)

Example 11

medium

Two forces act on an object:

\vec{F}_1 = 8 \text{ N}

east and

\vec{F}_2 = 6 \text{ N}

north. Find the magnitude and direction of the resultant force.

Find the magnitude and direction of the resultant force

Example 12

medium

Add

4

N east and

4

N east and

3

N west. Find the resultant.

Example 13

challenge

A boat is pushed

8

N east by motor and

6

N south by current, plus

6

N north by a tug. Net force magnitude and direction?

Find the net force on the boat from motor 8N east, current 6N south, and tug 6N north

Example 14

medium

15 \text{ N}

force points at

120°

measured counter-clockwise from the

+x

-axis. Find its components.

Find the components of the 15 N force at 120° from the +x axis

Example 15

medium

A vector has components

F_x=8

F_y=15

N. Find its magnitude.

Find the magnitude of the force from components Fx

Example 16

easy

Resolve a

10

N force at

0°

(along

x

) into

x

and

y

components.

Example 17

medium

Add the vectors:

\vec{A} = 5 \text{ m}

0°

(east) and

\vec{B} = 8 \text{ m}

90°

(north). Find the resultant.

Add vectors head-to-tail; find the magnitude and direction of the resultant

Example 18

medium

Resolve a

26

N force with

\cos\theta=5/13

\sin\theta=12/13

into components.

Resolve the 26 N force into its horizontal and vertical components

Example 19

hard

A plane is heading

30°

east of north at

200 \text{ km/h}

relative to the air. A wind blows due east at

40 \text{ km/h}

. Find the magnitude of the ground velocity.

Example 20

challenge

Vector

\vec A

7

east;

\vec B

24

north. Find the angle of

\vec A+\vec B

above east (use

\tan^{-1}

Find the angle that A + B makes above east

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Related Concepts

Displacement Velocity Force