Abaseball, which has a mass of 0.685 kg., is moving with a velocity of 38.0 m/s when it contacts the baseball bat duringwhich time the velocity of the ball becomes 57.0 m/s in the opposite direction. a. how much impulse has been delivered to the ball by the bat? while in contact with the bat the ball undergoes a maximum compression of approximately 1.0 cm. b. approximately how long did it take for the ball to be stopped by the bat? c. what will be the average force applied to the ball by the bat while stopping the ball?

Answers:

a)

b)

c)

Explanation:

According to the Impulse-Momentum theorem we have the following:

(1)

Where:

is the impulse

is the change in momentum

is the final momentum of the ball with mass and final velocity (to the right)

is the initial momentum of the ball with initial velocity (to the left)

So:

(2)

(3)

(4)

(5)

This time can be calculated by the following equations, taking into account the ball undergoes a maximum compression of approximately :

(6)

(7)

Where:

is the acceleration

is the length the ball was compressed

is the time

Finding from (7):

(8)

(9)

(10)

Substituting (10) in (6):

(11)

Finding :

(12)

According to Newton's second law of motion, the force is proportional to the variation of momentum   in time  :

(13)

(14)

Finally:

see earlier