In a Little League baseball game, the 145 g ball enters the strike zone with a speed of 13.0 m/s. The batter hits the ball, and it leaves his bat with a speed of 21.0 m/s in exactly the opposite direction.

1. what is the magnitude of the impulse delivered by the bat to the ball.

2. If the bat is in contact with the ball for 1.5ms , what is the magnitude of the average force exerted by the bat on the ball?

To answer these questions, we need to use the concept of impulse and average force.

1. The impulse delivered by the bat to the ball is equal to the change in momentum of the ball. The momentum of an object is given by the product of its mass and velocity.

The initial momentum of the ball is calculated by multiplying its mass (145 g = 0.145 kg) by its initial velocity (13.0 m/s):
Initial momentum = mass * initial velocity = 0.145 kg * 13.0 m/s

The final momentum of the ball is calculated by multiplying its mass (0.145 kg) by its final velocity (-21.0 m/s). Note that we take the negative sign because the final velocity is in the opposite direction:
Final momentum = mass * final velocity = 0.145 kg * (-21.0 m/s)

The change in momentum is equal to the final momentum minus the initial momentum:
Change in momentum = Final momentum - Initial momentum

To find the magnitude of the impulse, we can take the absolute value of the change in momentum.

2. The average force is calculated by dividing the impulse by the time duration of contact between the bat and the ball.

Average force = Impulse / Time duration

Given that the time duration of contact is 1.5 ms, we need to convert it to seconds by dividing it by 1000:
Time duration = 1.5 ms / 1000

Now, let's substitute the values into the formulas and perform the calculations to find the answers.