Question

if the velocity of a pitched ball has a magnitude of 47.5 m/s and the batted ball's velocity is 57.5 m/s in the opposite direction, find the magnitude of the change in momentum of the ball and of the impulse applied to it by the bat.

Answer 1

The magnitude of the change in momentum of the ball is equal to the magnitude of the initial momentum minus the magnitude of the final momentum. Therefore:

Change in momentum = |m1 * v1| - |m2 * v2|

where m1 and v1 are the mass and velocity of the pitched ball, and m2 and v2 are the mass and velocity of the batted ball. Since the direction of the batted ball is opposite to that of the pitched ball, we take the negative value of v2.

Substituting the given values, we get:

Change in momentum = |0.145 kg * 47.5 m/s| - |0.145 kg * (-57.5 m/s)|
= 14.0875 kg m/s + 8.3375 kg m/s
= 22.425 kg m/s

Therefore, the magnitude of the change in momentum of the ball is 22.425 kg m/s.

To find the impulse applied to the ball by the bat, we use the impulse-momentum theorem, which states that:

Impulse = Change in momentum

Substituting the value we obtained for the change in momentum, we get:

Impulse = 22.425 kg m/s

Therefore, the magnitude of the impulse applied to the ball by the bat is 22.425 kg m/s.