To solve this problem, we will break it down into two parts: first, we will find the velocity of the block mass \( m \) just before the collision, and then we will use the principles of momentum conservation and kinetic energy conservation to find the final velocities after the elastic collision.
### Step 1: Determine velocity \( v \) of block \( m \) just before collision
A block of mass \( m \) slides down a frictionless incline of angle \(