In a collision between two spheres $A$ and $B$, their velocities are symmetric ($v$ and $-v$, respectively) in the center-of-mass frame of reference. The final speed of $A$ does a $45°$ angle with its initial velocity.
Determine the final speed of the spheres if the collision is elastic, in the frame of reference where the sphere B is initially at rest.
How do I solve this? I am not used to solve these problems with the center-of-mass frame of reference.