Compression and output velocity

[Thundagere]

So, I'm launching foam balls using spinning wheels. The way it works is a sheet of polycarb is near the wheels. The ball is fed into the wheel and is compressed. The wheel turns and shoots the ball out.
My question is this. How should I calculate the output velocity of the ball? I know the torque of the motor, the dimensions of the wheel, the compression force in lbs of the ball, etc., but I need to calculate the output velocity of the ball and the velocity I want the wheel to spin at. Can someone explain these concepts to me?
Thanks for any help!

 

[Dr_Morbius]

The ball shoots out at the same velocity as the spinning wheel plus the rebound force generated by squeezing the ball.

 

[Thundagere]

How would I calculate the rebound force?