Question

a football punter accelerates from rest to a speed of 8 m/s during the time in which his toe is in contact with the ball (about 0.21 s). If the football has a mass of 0.50 kg, what average force does the punter exert on the ball?

Answer 1

The punter himself does not accelerate. The football does. So does his foot, but not as much as the ball does. If his own center of mass accelerated to 8 m/s in 0.21 seconds, we would be a world class sprinter.

The momentum change of the football,
8 m/s * 0.50 kg = 4.0 kg m/s
is equal to the impulse, F*0.21 s.

Solve for F.