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 vector V_1 of magnitude 13.4 m/s and angle theta_1 = 33.5 degree. Just after, it is traveling directly upward with velocity V_2 of magnitude 11.4 m/s. The duration of the collision is 2.40 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? (a) Number Units (b) Number Units (c) Number Units (d) Number Units

Explanation / Answer

Impulse = m (vf - vi)

vf = 11.4 j m/s

vi = 13.4 ( - cos33.5i - sin33.5j) = - 11.17i - 7.40j m/s

impulse = 0.3 ( 11.4j - (-11.17i - 7.40j))

= - 3.35i + 5.64j kg m/s

(A) magnitude = sqrt(3.35^2 + 5.64^2) = 6.56 kg m/s

(B) theta = 180 - tan^-1(5.64 / 3.35) = 120.7 deg

(C) impulse = F t

6.56 = F (2.40 x 10^-3)

F = 2733.33 N

(D) direction will be opposite of force on ball.

theta = 360 - 59.3 = 300.7 deg

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