The figure shows a 0.3 kg baseball just before and just after it collides with a

Question

The figure shows a 0.3 kg baseball just before and just after it collides with a bat. Just before, the ball has velocity v1 of magnitude 10.7 m/s and angle theta1 = 37.1 degree. Just after, it is traveling directly upward with velocity v2 of magnitude 9.00 m/s. The duration of the collision is 2.80 ms. What are the (a) magnitude and (b) direction (relative to the positive direction of the x axis) of the impulse on the ball from the bat? What re the (c) magnitude and (d) direction of the average force on the ball from the bat? (a) Number Units (b) Number Units (c) Number Units (d) Number Units

Explanation / Answer

v1 = 10.7*(-cos (37.1) i - sin (37.1)j) m/s

v2 = 9j m/s

mass = 0.3 kg

impulse = change in the momentum

impulse = 0.3 * (9j - 10.7*(-cos (37.1) i - sin (37.1)j))

impulse = 4.64 j + 2.56 i

magnitude of impulse on the wall = 5.3 kg.m/s

direction = arctan(4.64/2.56)

direction of the impulse on the wall = 61.1 deg

Average force = impulse/duration of collision

duration of collision = 2.80 ms

Average force = 5.3/(2.8 * 10^-3)

Average force on the ball = 1892.85 N

Direction of the average force = direction of the impulse

Direction of the average force on the ball = 61.1 deg

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