# Homework Help: Velocity from an elastic collision

Tags:
1. May 13, 2017

### Millie Baker

1. The problem statement, all variables and given/known data
A body X moving with a velocity v makes an elastic collision with a stationary body Y of equal mass on a smooth horizontal surface. Which statement gives the velocities of the two bodies after the collision? (multiple choice question)

3. The attempt at a solution
The answer according to the mark scheme is
velocity of X = 0
velocity of Y = v

So I can't understand how this is worked out. But this as far as I got:

MUx+MUy = MVx + MVy
Ux +Uy = Vx +Vy
Ux = Vx + Vy

How do you know that Vx is 0 and Vy is V (or Ux)?

2. May 13, 2017

### triso

You've used the conservation of momentum which is true for all collisions. Since the question specifies that it's an elastic collision, you know that kinetic energy will be conserved. Try including that in your equations.

3. May 13, 2017

### Millie Baker

Thank you, I understand now!

4. May 13, 2017

### haruspex

When you have conservation of both energy and momentum the two equations combined produce this neat result: the relative velocity reverses. I.e. v1f-v2f=v2i-v1i. See "Newton's Experimental Law" for a generalised version.