Three Pool Balls Homework - Find Final Velocities

[atarr3]

Homework Statement

A pool ball with initial speed v is aimed right between two other pools balls. If the the two right balls leave the elastic collision with equal speeds, find the final velocities of all three balls.

Homework Equations

Equations for Energy and Momentum conservation laws

The Attempt at a Solution

My questions for this problem are basically just which assumptions I can make. I'm assuming that the two right balls leave at equal angles, and the ball with the initial velocity is still traveling in the x-direction after the collision. But I'm not sure if I can assume this. And part of me wants to assume that the two right balls are deflected at 45 degree angles, but I'm also not sure if I can assume this.

These are my equations for momentum

$$mv = mv_{1} +2mv_{2}cos\theta$$ for the x-derection and the y-direction simplifies to 0 = 0. And for energy, after simplifications, I have $$v^{2} = v_{1}^{2} + 2v_{2}^{2}$$ , but I'm not sure where to go from this.

 

[atarr3]

Oh and the problem says that the three pool balls are of equal mass.