Developing a Softball Trajectory Model With Pneumatic Piston

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To develop a mathematical model for the speed of a softball struck by a pneumatic piston, start with Newton's second law, f = ma, where 'f' is the applied force, 'm' is the mass of the ball (0.188 kg), and 'a' is the acceleration. Calculate the acceleration by rearranging the formula to a = f/m, using forces ranging from 170 lb to 500 lb (converted to Newtons). The resulting acceleration can then be used to determine the final velocity of the ball upon impact. This model will provide the necessary data for further computations in the larger project. Understanding the relationship between force, mass, and acceleration is crucial for accurate trajectory predictions.
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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.
 
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Start off by writing f = ma for the ball.
 

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