A baseball with a mass od 140 g is pitched so that it crosses home plate with a

Question

A baseball with a mass od 140 g is pitched so that it crosses home plate with a speed of 92.0 mph at an angle of 18.4° below the horizontal. It is hit directly back up the middle of the field with a speed of 81.0 mph at an angle of 41.3° above the horizontal. Find (a) the impulse (magnitude and direction) delivered to the ball by the bat, and (b) the magnitude of the average force on the ball, if the bat was in contact with the ball for 32.0 ms.

The answers (a) 10.6 N-s, 29.1° above the horizontal (b) 331 N

Can you please show a detail explanation of the work you do to get those answers.

Explanation / Answer

Refer below figure,

a) m=0.14kg

vi= 92.0mph = 41.13m/s , qi= -18.4 deg

vf=81.0mh= 36.21m/s, qf= 41.3 deg

P= Pf – Pi

Px= Pfx– Pix = m(vfcosqf -vicosqI) = 0.14(36.21cos(41.3) – 41.13cos(180+18.4)) = 9.27 kg*m/s

Py= Pfy– Piy = m(vfsinqf -visinqI) = 0.14(36.21sin(41.3) – 41.13sin(180+18.4)) = 5.16 kg*m/s

P= sqrt(Px^2+ Py^2) = sqrt(9.27^2+5.16^2) = 10.6 N.s

q= tan^-1(Py/ Px) = tan^-1(9.27/5.16) = 29.1 deg (above the horizontal)

b) F= P/ t = 10.6/(32*10^-3) = 331 N

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