## Let's break down the steps for each problem to help you understand them better.

1) For the first problem:

a) To find how long the collision lasts, you can use the equation T = 2X/V, where T is the duration of the collision, X is the distance traveled during the collision (1.2m in this case), and V is the initial velocity of the car (25.0m/s).

Plug in the values: T = 2(1.2) / 25.0 = 0.096 seconds.

b) To find the magnitude of the average force on the car, you can calculate it using the equation F = M * a, where F is the average force, M is the mass of the car (1400 kg), and a is the acceleration.

The acceleration can be found using the equation a = V^2 / (2X), with V as the initial velocity (25.0 m/s) and X as the distance during the collision (1.2m).

Plug in the values: a = (25.0^2) / (2 * 1.2) = 520.83 m/s^2.

Now, use F = M * a: F = 1400 kg * 520.83 m/s^2 = 729,166.67 N.

c) To find the acceleration of the car in g's, divide the acceleration (a) by the acceleration due to gravity (g = 9.8 m/s^2).

Divide the acceleration a = 520.83 m/s^2 by g: a_in_g = 520.83 m/s^2 / 9.8 m/s^2 = 53.15 g's.

2) For the second problem:

a) To find the impulse delivered to the ball, you can use the fact that the impulse is equal to the change in momentum. Momentum is given by the equation p = m * v, where p is the momentum, m is the mass of the ball (0.15 kg), and v is the final velocity.

When the ball is hit and changes direction, the final velocity becomes -22 m/s. So, the change in momentum is (0.15 kg * -22 m/s) - (0.15 kg * 20 m/s) = -4.8 kgÂ·m/s.

b) To find the average force exerted by the bat on the ball, you can use the equation average force = impulse / time.

The impulse is the change in momentum from part a) (-4.8 kgÂ·m/s), and the time force is applied is given as 2.0 x 10^-3 seconds.

Calculate the average force: average force = -4.8 kgÂ·m/s / (2.0 x 10^-3 s) = -2400 N.

Make sure to double-check your calculations and units to ensure accuracy. If your answers still do not match the book, there might be a slight discrepancy due to rounding or a different approach used in the book.