# Elastic collision / relative velocity problem [closed]

I'm having some trouble with a homework exercise and I'd really appreciate some help! I've done the first part correctly (according to the solution sheet), but I can't seem to get the second part right.

**The first part of the problem:

Two particles collide elastically. If m1 = 2 kg and m2 = 1 kg and the initial velocities of the two particles are u1 = (3i + 4j) ms-1 and u2 = (7i + j) ms-1 respectively, find (i) the velocity of the centre of mass and (ii) the momentum of each particle in the centre-of-mass frame.**

Okay, so far I have:

i) V(CM) = (13/3i + 3j)ms-1 & (ii) p'(1,2) = +/-(8/3i - 2j)kgms-1

**The second part of the problem:

After the elastic collision, the particles separate so that particle 1, as viewed from particle 2, moves away along the positive x-axis (i.e. in the direction of the unit vector i). Find the final velocity of each particle in the laboratory frame.**

This is where I'm getting confused.

To find the final velocities v1 and v2 (and knowing that the collision is elastic so V(rel) = -U(rel)), I used the equations:

v'1 = (m2/M)*V(rel) -----> v1 = v'1 + V(CM) & v'2 = -(m1/M)*V(rel) -----> v2 = v'2 + V(CM)

Which gives me the values:

v1 = (4/3i - j)ms-1 & v2 = (17/3i + 2j)ms-1

Which, according to the solution sheet are incorrect. The correct values are in fact:

v1 = (6i + 3j)ms-1 & v2 = (i + 3j)ms-1

Now I know I'm obviously missing something here, but I'm not sure what. Could somebody please explain this to me? Is it something to do with the information given on how particle 1 moves away along the positive x-axis relative to particle 2?

I've spent a while trying to solve this so any help would be greatly appreciated (sorry for long post)!

Thank you

## closed as off-topic by Danu, John Rennie, Carl Witthoft, dmckee♦Feb 7 '16 at 17:12

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – Danu, John Rennie, Carl Witthoft, dmckee
If this question can be reworded to fit the rules in the help center, please edit the question.