A pitcher throws a fast ball of 85 mph toward a batter. The bat strikes the ball

Question

A pitcher throws a fast ball of 85 mph toward a batter. The bat strikes the ball at the bat's "sweet spot" such that the ball leaves the bat traveling over the pitcher's head at 120 mph on its way to a standup homerun. High speed video of the batter shows that the ball was in contact with the bat during 8 frames of a video running at 120 frames per second.

A. What is the ball's change in velocity during it contact with the bat?

B. What was the acceleration delivered to the ball by the bat during their contact?

Explanation / Answer

Initial velocity, V1 = 85 mph = 38 m/s Final velocity, V2 = 120 mph = 53.6 m/s Time taken for running 1 frame, t = ( 1 /120 ) s Time taken for 8 frames = ( 8 / 120 ) s = 0.067 s Time of contact of ball in contact with bat, T = 0.067 s (a) Change in velocity = V2 + V1 [ since they are in opposite direction ] = 91.6 m/s (b) Acceleration = Change in velocity / Time of contact = 91.6 / 0.067 = 1367.2 m/s^2

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