A baseball mass of 150.0g, is thrown by the pitcher toward the home plate with a velocity of 45.0 m/s. it is hit back at the pitcher with a velocity of 60.0 m/s, what is the average force on the bat, if the ball and bat are in contat for a time of 100.0 ms? What is the change in kinetic energy of the ball?

To calculate the average force on the bat, we can use the impulse-momentum theorem:

1. First, we need to find the initial momentum of the baseball. The momentum (p) is calculated by multiplying the mass (m) of the baseball by its initial velocity (v). Since the mass is given as 150.0g, we need to convert it to kilograms:
mass = 150.0 g = 0.150 kg
initial velocity = 45.0 m/s
initial momentum (p) = mass * initial velocity

2. Next, we find the final momentum of the baseball. The final momentum is calculated by multiplying the mass of the baseball by its final velocity. Since the mass doesn't change after being hit, the final momentum is equal to the initial momentum:
final velocity = 60.0 m/s
final momentum = mass * final velocity

3. The change in momentum can be calculated by subtracting the initial momentum from the final momentum:
change in momentum = final momentum - initial momentum

4. The average force can be determined using the equation F = change in momentum / time. However, the time needs to be in seconds, so we'll convert 100.0 ms to seconds:
time = 100.0 ms = 100.0 * 10^-3 s

5. Finally, we can calculate the average force on the bat:
average force (F) = change in momentum / time

To find the change in kinetic energy of the ball, we can use the equation for kinetic energy:

6. The initial kinetic energy (K1) of the ball can be calculated using the equation K1 = (1/2) * mass * (initial velocity)^2.

7. The final kinetic energy (K2) of the ball can be calculated using the equation K2 = (1/2) * mass * (final velocity)^2.

8. The change in kinetic energy can be found by subtracting the initial kinetic energy from the final kinetic energy:
change in kinetic energy = K2 - K1.

Now that we have all the necessary equations and information, you can go ahead and calculate the average force on the bat and the change in kinetic energy of the ball.