# Momentum question asking ratio of final 2 velocities

## Homework Statement

A cart mass of M moving at 3V (right) collides with a stationary mass of M, Determine the ratio of the two final velocities if the collision is elastic

p=mv
ek=(mv^2/2)

## The Attempt at a Solution

m1v1=m1v1'+m2v2'

Since the masses are all equal and v1 is 3V the equation becomes
3 = v1' + v2'

Since the collision is elastic the total energy afterwards equals the total energy afterwards

Ek=(mv^2/2)

so Ek1=Ek1'Ek2'
and since every term is over 2,and the masses equal the equation simplifies to
v1^2=v1'^2+v2^2

After rearranging the first equation you get v1' = v2'-3, and then plug that into the energy equation to get
9= 2v2'^2 -6v2-9
0=2v2'^2 -6v2

after applying the quadratic equation you get 3 or 0, and since the velocity has to change v2' is 3, subsequently v1' is 0 so the ratio is 3:0, or 0:3

3:0 doesn't make sense to me for some reason but I can't find any mistake in what I did, is this right?

BvU
Homework Helper
I can't find a mistake either.
Check it by sliding a coin against a similar coin on a flat table (aim for a central collision)

By the way: if an initial speed of 3V is given, your calculations should be in units of V, e.g.
3 MV = MV1'+ MV2'

haruspex