Collisions Examples: 47 Problems with Answers

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

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

Concept Recap

A collision is an interaction in which objects exert large forces on each other for a short time, changing their momenta.

During a crash or bounce, forces act briefly but strongly, so motion can change a lot.

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: Collisions works by defining the interacting system and comparing motion before and after the interaction.

Common stuck point: Students often know a formula related to collisions 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

medium

1 \text{ kg}

cart at

6 \text{ m/s}

collides elastically head-on with a

1 \text{ kg}

cart at rest. Find both velocities afterward.

Answer

v_{1}^{'} = 0, v_{2}^{'} = 6 m/s

First step

Equal-mass elastic head-on: velocities swap.

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Example 2

medium

1500 \text{ kg}

car at

20 \text{ m/s}

collides with a

1000 \text{ kg}

car at rest; they stick. Find the wreck's speed and the KE lost.

Example 3

hard

0.5 \text{ kg}

ball is dropped from

1.8 \text{ m}

and rebounds to

1.25 \text{ m}

. Find the coefficient of restitution. (

g=10

)

Example 4

challenge

Ball A (

1 \text{ kg}

) at

4 \text{ m/s}

hits ball B (

1 \text{ kg}

) at rest, and after the collision ball A moves at

30°

above the original line at

2\sqrt{3} \text{ m/s}

. Find ball B's velocity vector.

Practice Problems

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

Example 1

easy

What single quantity is conserved in every collision (no external forces)?

Example 2

easy

A 2 kg ball at

5\,\text{m/s}

hits a 2 kg ball at rest. Total momentum before the collision is what?

Example 3

easy

A 3 kg object moves at

4\,\text{m/s}

. Find its momentum.

Example 4

easy

Two objects approach each other with momenta

+8\,\text{kg}\cdot \text{m/s}

and

-3\,\text{kg}\cdot \text{m/s}

. Find the total momentum.

Example 5

easy

In a collision, is the force between objects large for a long or short time?

Example 6

easy

Impulse on an object equals its change in what?

Example 7

easy

A 0.5 kg ball changes velocity from

0

6\,\text{m/s}

in a collision. Find the impulse on it.

Example 8

easy

Why do airbags reduce injury in a collision?

Example 9

medium

A 2 kg ball at

6\,\text{m/s}

collides with a 4 kg ball at rest. After, the 2 kg ball moves at

2\,\text{m/s}

(same direction). Find the 4 kg ball's velocity.

Example 10

medium

A 1 kg ball at

10\,\text{m/s}

hits a 1 kg ball at rest; afterward they both move at

5\,\text{m/s}

. Is this collision elastic?

Example 11

medium

A 0.15 kg baseball hits a bat at

40\,\text{m/s}

and rebounds at

30\,\text{m/s}

. Find the magnitude of the impulse delivered.

Example 12

medium

A 1200 kg car at

15\,\text{m/s}

and an 800 kg car at

-10\,\text{m/s}

collide head-on. Find the total momentum (which way?).

Example 13

medium

A 0.2 kg ball experiences a constant force of

50\,\text{N}

for

0.04\,\text{s}

during a collision. Find its change in velocity.

Example 14

medium

A 3 kg object at

4\,\text{m/s}

collides with a 2 kg object at

-1\,\text{m/s}

. If they stick, find their common velocity.

Example 15

medium

A 0.05 kg dart at

20\,\text{m/s}

embeds in a 0.95 kg block at rest on a frictionless surface. Find the common speed.

Example 16

medium

A 4 kg object at

3\,\text{m/s}

collides with a 2 kg object at rest; afterward the 4 kg moves at

1\,\text{m/s}

(same direction). Find the 2 kg object's velocity.

Example 17

medium

A 0.3 kg ball hits a wall at

8\,\text{m/s}

and rebounds at

6\,\text{m/s}

. Find the magnitude of the impulse on the ball.

Example 18

challenge

A 2 kg ball at

5\,\text{m/s}

collides elastically with a 3 kg ball at rest. Use

v_1' = \frac{m_1-m_2}{m_1+m_2}v_1

and

v_2' = \frac{2m_1}{m_1+m_2}v_1

to find both velocities.

Example 19

challenge

A 1 kg ball moving at

8\,\text{m/s}

strikes two stationary balls in a line elastically (Newton's cradle, all 1 kg). After the chain, how many balls move and at what speed?

Example 20

challenge

A 4 kg block at

3\,\text{m/s}

collides with a 2 kg block at

-3\,\text{m/s}

; they stick, then slide onto a rough surface with

\mu_k = 0.25

(

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

). Find the stopping distance.

Example 21

easy

1.5 \text{ kg}

object moves at

4 \text{ m/s}

. Find its momentum.

Example 22

easy

Two

2 \text{ kg}

objects move toward each other, each at

3 \text{ m/s}

. Find the total momentum of the system.

Example 23

easy

Impulse

J = 8 \text{ N}\cdot \text{s}

acts on a

2 \text{ kg}

cart at rest. Find its final speed.

Example 24

easy

0.4 \text{ kg}

ball's velocity changes from

+5 \text{ m/s}

-3 \text{ m/s}

after hitting a wall. Find the impulse on the ball.

Example 25

easy

0.5 \text{ kg}

ball collides with a wall, experiencing

30 \text{ N}

for

0.1 \text{ s}

. Find the impulse magnitude.

Example 26

medium

3 \text{ kg}

cart at

4 \text{ m/s}

collides with and sticks to a

5 \text{ kg}

cart at rest. Find their common speed after.

Example 27

medium

0.06 \text{ kg}

tennis ball is hit by a racket: it comes in at

25 \text{ m/s}

and leaves at

-30 \text{ m/s}

. Find the impulse on the ball.

Example 28

medium

Two carts on a frictionless track:

m_1 = 2 \text{ kg}

+3 \text{ m/s}

m_2 = 1 \text{ kg}

-6 \text{ m/s}

. They stick. Find the final velocity.

Example 29

medium

0.05 \text{ kg}

bullet at

400 \text{ m/s}

embeds in a

2 \text{ kg}

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

Example 30

medium

2 \text{ kg}

ball at

5 \text{ m/s}

collides head-on elastically with a

2 \text{ kg}

ball at

-3 \text{ m/s}

. Find both velocities afterward.

Example 31

medium

0.2 \text{ kg}

ball traveling at

10 \text{ m/s}

strikes a wall and rebounds at

-8 \text{ m/s}

. Contact lasts

0.05 \text{ s}

. Find the average force.

Example 32

medium

A force vs. time graph shows a triangular pulse: peak

40 \text{ N}

0.05 \text{ s}

, returning to zero at

0.10 \text{ s}

. Find the impulse.

Example 33

medium

An astronaut (mass

80 \text{ kg}

) at rest throws a

2 \text{ kg}

wrench at

5 \text{ m/s}

in space. Find the astronaut's recoil speed.

Example 34

hard

3 \text{ kg}

ball at

5 \text{ m/s}

collides elastically head-on with a

1 \text{ kg}

ball at rest. Find both velocities afterward.

Example 35

hard

0.01 \text{ kg}

bullet at

500 \text{ m/s}

embeds in a

1 \text{ kg}

block hanging from a string (ballistic pendulum). Find how high the block rises. (

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

)

Example 36

hard

2 \text{ kg}

puck moving at

4 \text{ m/s}

east collides and sticks to a

3 \text{ kg}

puck moving at

2 \text{ m/s}

north on a frictionless surface. Find the speed of the combined object.

Example 37

hard

1 \text{ kg}

cart moving at

8 \text{ m/s}

collides perfectly inelastically with a

3 \text{ kg}

cart at rest. Find the fraction of initial KE retained.

Example 38

hard

0.05 \text{ kg}

bullet at

300 \text{ m/s}

passes through a

2 \text{ kg}

block and exits at

100 \text{ m/s}

. The block sits on a frictionless surface. Find the block's speed afterward.

Example 39

hard

0.3 \text{ kg}

ball hits a wall horizontally at

10 \text{ m/s}

and bounces back at

-8 \text{ m/s}

. Contact lasts

0.04 \text{ s}

. Find the average force on the wall.

Example 40

hard

4 \text{ kg}

object at

6 \text{ m/s}

collides elastically with a stationary

2 \text{ kg}

object. Find both speeds afterward.

Example 41

hard

2 \text{ kg}

block slides at

4 \text{ m/s}

into a

1 \text{ kg}

block at rest. They stick and slide onto a rough surface with

\mu_k = 0.2

(

g=10

). Find their stopping distance.

Example 42

challenge

A neutron (mass

1 \text{ u}

) collides elastically head-on with a stationary carbon-12 nucleus (mass

12 \text{ u}

). Find the fraction of the neutron's kinetic energy transferred to carbon.

Example 43

challenge

1 \text{ kg}

ball is dropped onto a hard floor from

5 \text{ m}

and bounces with coefficient of restitution

0.8

. After many bounces, find the total distance traveled before coming to rest. (

g=10

)

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Related Concepts

Impulse Conservation of Momentum Elastic Collision Inelastic Collision

Background Knowledge

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

impulseconservation of momentum