Answer:The croquet ball velocity v will be 56/500 the tennis ball velocity V after the impulse.
The second law (force = mass*acceleration) says that the same force will accelerate the balls by the inverse of their mass. That is, the force will continuously change the momentum:
f = 500a = 56A
Therefore a = f/500 and A = f/56
and a/A = 56/500.
The croquet ball will accelerate less, for whatever time or distance you apply the force.
The third law: for every action, there is an equal and opposite reaction. So, if in fact you apply the same force to strike each ball, you will feel the same reaction. That’s probably easier to do for a quick strike (the impulse case above) than for a long, smooth acceleration over distance, because the balls have very different elastic response. The body can tell how equally you applied force!
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