Developing a Softball Trajectory Model With Pneumatic Piston

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JayDavis
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I am a hack at this, so I am turning to you guys for help.

I need to develop a mathematical model do generate the speed of a softball when struck with differing amounts of force.

The specs are:
weight of ball 188g
applied force 170 lb to 500 lb

The force is applied by a pneumatic piston that strikes the ball.

How do I do this?

The end result will be fed into a larger computation.
 
Start off by writing f = ma for the ball.