# Relative Velocity after collision

• merced
In summary, when two balls of the same mass collide with a relative velocity of 10 m/s, their individual velocities become equal and opposite, with one ball having a velocity of 5 m/s and the other having a velocity of -5 m/s. However, their relative velocity after the collision is still 10 m/s because the balls simply exchanged their velocities. This is due to the concept of conservation of momentum and energy in an elastic collision.
merced
"Two balls of the same mass approach each other with a relative velocity of 10 m/s, what is their relative velocity after the collision, which is presumed elastic?"

I assumed that the balls have equal and opposite velocities of 10 m/s.
Should the individual velocities be 5 m/s and -5 m/s (because 10 m/s is the relative velocity)?

When I solved the problem, the balls simply exchanged their velocities.

I said that their relative velocities after the collision are 10 m/s. However, this is wrong because there is only one relative velocity.
I think I have the concept wrong. Please clarify.

Solve the equations of conservation of momentum and conservation of energy (since this collision is elastic) for the relative velocities before and after the collision, and you will see the relationship.

Dorothy

Your understanding of the concept is correct. In this scenario, the relative velocity after the collision would still be 10 m/s because the balls simply exchanged their velocities. However, it is important to note that the individual velocities of the balls would have changed. One ball would now have a velocity of -5 m/s and the other would have a velocity of 5 m/s. The relative velocity refers to the velocity of one object relative to the other, and in this case, it remains the same.

## What is relative velocity after collision?

Relative velocity after collision is the velocity of an object in relation to another object after they have collided. It takes into account the velocities of both objects before and after the collision.

## How is relative velocity calculated after collision?

Relative velocity can be calculated using the formula Vr = V1 - V2, where Vr is the relative velocity, V1 is the velocity of the first object, and V2 is the velocity of the second object. This formula assumes a one-dimensional collision.

## Does relative velocity after collision depend on the mass of the objects?

No, relative velocity after collision does not depend on the mass of the objects involved. It only depends on their initial velocities and the type of collision (elastic or inelastic).

## What is the difference between elastic and inelastic collisions?

In an elastic collision, both kinetic energy and momentum are conserved, meaning that the objects bounce off each other with no loss of energy. In an inelastic collision, kinetic energy is not conserved and some energy is lost as heat or sound.

## How does relative velocity after collision relate to conservation of momentum?

Relative velocity after collision is closely related to the principle of conservation of momentum, which states that in a closed system, the total momentum before and after a collision remains constant. This means that the sum of the relative velocities before and after the collision must be equal.

### Similar threads

• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
735
• Introductory Physics Homework Help
Replies
20
Views
1K
• Introductory Physics Homework Help
Replies
11
Views
1K
• Introductory Physics Homework Help
Replies
335
Views
8K
• Introductory Physics Homework Help
Replies
1
Views
656
• Introductory Physics Homework Help
Replies
10
Views
1K
• Introductory Physics Homework Help
Replies
29
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
1K
• Introductory Physics Homework Help
Replies
17
Views
968