Elastic collision with 3 pool balls

[KaiserBrandon]

Homework Statement

A pool ball with initial speed v is aimed right between two other pool balls (looks like:

0 -> :


if the semicolon were two balls and were touching each other).

If the two right balls leave the elastic collision with equal speeds, find the final velocities of all three balls.

Homework Equations

k=1/2m(v^2)
p=mv

The Attempt at a Solution

All I need to know is if I should assume that the right balls have a final velocity at an angle 45 and -45 degrees to the horizontal.

 

[ideasrule]

No, don't assume that. Just assume that the two balls leave at the same angle to the horizontal and at the same speed.

 

[KaiserBrandon]

ok, so then with momentum and energy conservation, I get the equations:
v1=(2V)cos(theta) + v1f
and
v1^2=2V^2 + (v1f)^2

where v1 is the initial velocity of the incoming ball, V is the final speed of the two right balls, and v1f is the final speed of the first ball. I don't know how what I can do to get an expression for the velocities.

 

[Mindscrape]

What do you mean you don't know how to get an expression for the velocities?