Question

In a slow-pitch softball game, a 0.200 kg softball crossed the plate at 10.00 m/s at an angle of 45.0° below the horizontal. The batter hits the ball toward center field, giving it a velocity of 44.0 m/s at 30.0° above the horizontal.

If the force on the ball increases linearly for 4.00 ms, holds constant for 20.0 ms, then decreases to zero linearly in another 4.00 ms, what is the maximum force on the ball?
(magnitude)
° (above the horizontal)

Answer 1

First compute the momentum change on the ball, by subtracting the incoming momentum vector from the hit ball's momentum vector.

Calculate the magnitude of the momentum change. That is the impulse delivered to the ball.

Finally, figure out the maximum force, which is the constant force from 4 to 24 ms, by setting the area under the Force-time curve equal to the impulse.

Impulse integral
= 20ms*Fmax + 4ms*Fmax/2 +4ms*Fmax/2
= 24ms*Fmax