A baseball is pitched toward a batter. The batter hits it, knocking the ball bac

Question

A baseball is pitched toward a batter. The batter hits it, knocking the ball back over the pitcher’s head. Just before the batter hits it, it is traveling at 40 m/s parallel to the ground. After the batter hits it, it is traveling at 60 m/s at an angle 30 degrees above the horizontal.

The bat is in contact with the ball for 10 milliseconds; assume that the bat exerts a constant force on the ball during this time. If the ball has a mass of 145 grams, what is the size of this force, and in what direction does it point?

Explanation / Answer

We know that force = change in momentum / time

Initial velocity = 40 m/s towards batter at parallel to ground +x

Final velocity = 60 m/s at an angle to 30 deg above the ground -x =

-60cos30 in +x direction = -51.96 m/s

change in momentum = 0.145*(40-(-51.96)) = 13.33 kg. m/s outwards batter

Force = 13.33 / 10x10^-3 s = 1333.44 N. outwards batter................Ans.

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