Momentum of a collision in 2-D

[sodr2]

1. The problem statement, all variables and given/known data
If you have a mass colliding with another mass at rest and they both go off in different directions, how do you find out the velocity of the masses after the collision given the distance they travel, the angle they travel and the masses (m1 = m2). You are also told that momentum is proportional to velocity which is proportional to distance.


2. Relevant equations
P(total) = P(total)¹

m1v1 = m1v1¹ + m2v2¹


3. The attempt at a solution
Im guessing that the horizontal component of their velocity remains unchanged and therefore the distance they go horizontally is propotional to their horizontal velocity, but I still dont understand how you can determine the velocity of the masses with this information.

I was told that the distance the masses travel after collision represents the final momentum vectors of mass 1 & 2 because m1 = m2 and p is proportional to v, proportional to d. Could I take the distance they travel and divide it by thier masses to get the velocity because p=mv????

[rootX]

I think it is about using
m1d1 = m1d1¹ + m2d2¹

divide them into x-y components

[sodr2]

Ok, that looks like the right way to do it, but Im almost sure that for equal size balls with the same mass, the displacement lengths can be used in place of the momentum. How can the displacement equal momentum, when youre saying that momentum equals displacement AND mass? Mabey since the masses are the same before and after, could you take out masses?