Momentum Examples: 46 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Momentum.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The product of an object's mass and velocity, representing the quantity of motion it carries.

How hard it is to stop something moving. Heavy and fast = lots of momentum.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Momentum works by defining the interacting system and comparing motion before and after the interaction.

Common stuck point: Students often know a formula related to momentum but skip the recognition step: Is the interaction short, collision-like, or rotational, and have I checked whether external forces or torques can be ignored? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Is the interaction short, collision-like, or rotational, and have I checked whether external forces or torques can be ignored?

Worked Examples

Example 1

easy

2 \text{ kg}

ball moves at

5 \text{ m/s}

. What is its momentum?

Answer

p = 10 kg m/s

First step

Recall the momentum formula:

p = mv

, where

m

is mass and

v

is velocity.

Full solution

2
Identify the given values: $m = 2 \text{ kg}$ , $v = 5 \text{ m/s}$ .
3
Substitute and calculate: $p = 2 \times 5 = 10 kg m/s$

Momentum is the product of mass and velocity. It is a vector quantity, meaning it has both magnitude and direction.

Example 2

medium

1500 \text{ kg}

car moving at

20 \text{ m/s}

and a

0.05 \text{ kg}

bullet moving at

600 \text{ m/s}

. Which has greater momentum?

Example 3

medium

2 \text{ kg}

cart moving east at

3 \text{ m/s}

is pushed and reaches

7 \text{ m/s}

east. Find the change in momentum.

Example 4

medium

4 \text{ kg}

object moves at

3 \text{ m/s}

east. A

2 \text{ kg}

object moves at

6 \text{ m/s}

west. Find the total momentum (take east positive).

Example 5

hard

60 \text{ kg}

person stands on a

40 \text{ kg}

raft, both at rest. The person walks at

1.5 \text{ m/s}

east relative to the ground. Find the raft's velocity (frictionless water).

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

What velocity must a

0.5 \text{ kg}

ball have to possess a momentum of

15 \text{ kg m/s}

Example 2

medium

1200 \text{ kg}

car moves east at

25 \text{ m/s}

while a

1000 \text{ kg}

car moves west at

10 \text{ m/s}

. What is the total momentum of the two-car system?

Example 3

easy

2

kg ball moves at

5

m/s. What is its momentum?

Example 4

easy

1500

kg car travels at

20

m/s. Find its momentum.

Example 5

easy

0.5

kg ball has momentum

4

\cdot

m/s. What is its speed?

Example 6

easy

A ball moving right has momentum

+6

\cdot

m/s. What is the momentum of an identical ball moving left at the same speed?

Example 7

easy

3

kg object has momentum

15

\cdot

m/s. What is its velocity?

Example 8

easy

Which has more momentum: a

2

kg ball at

6

m/s or a

4

kg ball at

2

m/s?

Example 9

easy

10

kg cart at rest is given a push to

3

m/s. What is its final momentum?

Example 10

easy

0.2

kg arrow flies at

40

m/s. Find its momentum.

Example 11

medium

2

kg ball changes velocity from

+3

m/s to

-1

m/s. Find its change in momentum.

Change in momentum Δp connects p_i to p_f; reversing part of the velocity produces a large negative Δp.

Example 12

medium

4

kg object moving at

5

m/s has the same momentum as a

2

kg object. What is the lighter object's speed?

Example 13

medium

0.15

kg baseball at

30

m/s is caught and stopped. What is the magnitude of its momentum change?

Example 14

medium

Two balls:

3

kg at

+4

m/s and

2

kg at

-5

m/s. What is the total momentum of the system?

Example 15

medium

1200

kg car at

15

m/s and a

800

kg car at

15

m/s travel the same way. Find the total momentum.

Example 16

medium

0.5

kg ball hits a wall at

8

m/s and bounces back at

6

m/s. Find the magnitude of its momentum change.

Example 17

medium

2

kg object moving east at

3

m/s turns to move north at

4

m/s. Find the magnitude of its momentum change.

Example 18

medium

0.06

kg tennis ball has momentum

2.4

\cdot

m/s. Find its kinetic energy.

Example 19

medium

0.1

kg ball at

20

m/s is caught by a

4.9

kg glove (initially at rest) and they move together. Find the common speed.

Example 20

challenge

Two equal-mass balls move toward each other, each at

4

m/s. They stick together. Find their common velocity (closed system).

Example 21

challenge

3

kg object at

4

m/s and a

1

kg object at rest. After collision the

3

kg moves at

2

m/s (same direction). Find the

1

kg object's velocity.

Example 22

challenge

0.1

kg ball moving at

20

m/s is struck and reverses to

25

m/s in

0.01

s. Find the average force on it.

Example 23

easy

5 \text{ kg}

object moves at

3 \text{ m/s}

. What is its momentum?

Example 24

easy

0.05 \text{ kg}

bullet flies at

400 \text{ m/s}

. Find its momentum.

Example 25

easy

1.2 \text{ kg}

ball has a momentum of

6 \text{ kg} \cdot \text{m/s}

. Find its speed.

Example 26

easy

A bicycle and rider have a total mass

80 \text{ kg}

and move at

4 \text{ m/s}

. What is their momentum?

Example 27

medium

0.05 \text{ kg}

bullet at

300 \text{ m/s}

embeds in a

2.95 \text{ kg}

block at rest on a frictionless surface. Find the combined speed afterward.

Example 28

medium

0.3 \text{ kg}

ball moving at

5 \text{ m/s}

hits a wall and bounces back at

3 \text{ m/s}

. Find

|\Delta p|

Example 29

medium

Two skaters of masses

50 \text{ kg}

and

70 \text{ kg}

stand at rest. They push off and the

50 \text{ kg}

skater moves at

1.4 \text{ m/s}

east. Find the

70 \text{ kg}

skater's velocity.

Example 30

medium

A net force of

4 \text{ N}

acts on a

2 \text{ kg}

object for

3 \text{ s}

. Find the change in momentum.

Example 31

medium

1500 \text{ kg}

car slows from

20 \text{ m/s}

5 \text{ m/s}

. Find the magnitude of the change in momentum.

Example 32

medium

3 \text{ kg}

object moving north at

5 \text{ m/s}

is acted on by a

6 \text{ N}

force north for

2 \text{ s}

. Find its final velocity.

Example 33

medium

0.1 \text{ kg}

ball is dropped and hits the ground at

10 \text{ m/s}

, then rebounds at

8 \text{ m/s}

. Find the impulse the ground delivers to the ball.

Example 34

hard

3 \text{ kg}

object at

6 \text{ m/s}

collides with a

1 \text{ kg}

object at rest. They stick. Find the common final velocity.

Example 35

hard

0.5 \text{ kg}

ball moving east at

4 \text{ m/s}

and a

0.5 \text{ kg}

ball moving north at

3 \text{ m/s}

collide and stick together. Find the magnitude of their common velocity.

The two perpendicular momenta combine as components; the resultant magnitude gives the common speed after sticking.

Example 36

hard

0.2 \text{ kg}

ball is struck and changes velocity from

-15 \text{ m/s}

+25 \text{ m/s}

0.02 \text{ s}

. Find the average force on the ball.

Example 37

hard

80 \text{ kg}

astronaut in space throws a

2 \text{ kg}

tool at

10 \text{ m/s}

relative to the ground. Find the astronaut's recoil speed (starting at rest).

Example 38

hard

1000 \text{ kg}

car moving at

20 \text{ m/s}

east hits a stationary

1500 \text{ kg}

truck; they stick. Find their common speed.

Example 39

hard

0.4 \text{ kg}

object moving at

5 \text{ m/s}

east elastically collides head-on with a

0.6 \text{ kg}

object at rest. Find the velocity of the

0.4 \text{ kg}

object after.

Example 40

challenge

Two equal-mass carts collide elastically: cart A at

6 \text{ m/s}

hits stationary cart B. Find the velocities of both after the collision.

Example 41

challenge

0.15 \text{ kg}

baseball at

40 \text{ m/s}

is caught and brought to rest in

0.05 \text{ s}

. Compare the average force to the ball's weight (

g = 10 \text{ m/s}^2

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Related Concepts

Mass Velocity Impulse Conservation of Momentum

Background Knowledge

These ideas may be useful before you work through the harder examples.

massvelocity