The figure shows a 0.3 kg baseball just before and just after it collides with a
ID: 1448783 • Letter: T
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 ModifyingAbove v With right-arrow Subscript 1 of magnitude 12.2 m/s and angle 1 = 37.4°. Just after, it is traveling directly upward with velocity ModifyingAbove v With right-arrow Subscript 2 of magnitude 10.0 m/s. The duration of the collision is 2.70 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 are the (c) magnitude and (d) direction of the average force on the ball from the bat?
Explanation / Answer
initial velcocity, vi = 12.2 ( - cos37.4i - sin37.4j )
vi = - 9.69i - 7.41j
final velocity, vf = 0 i + 10j
a) Impulse = change in momentum = m vf - mvi
= m (vf - vi) = 0.3 ( 9.69i + 17.4j)
= 2.91i + 5.22 j
magnitude = sqrt(2.91^2 + 5.22^2) = 5.97 kg m /s
b) direction = tan^-1(5.22 / 2.91) = 60.9 deg
c) Impulse = F x time
F = 2.91i + 5.22 j / (2.70 x 10^-3) = 1077.8i + 1933.3 j N
magnitude = 2213.46 M
d) direction same as impulse
@ = 60.9 deg