the instant before a batter hits a 0.14 kilogram baseball, the velocity of the ball is 45 m/s west. the instant after the batter hits the ball, the ball's velocity is 35 m/s. The bat and ball are in contact for 1.0*10^-2.

1. determine the magnitude and direction of the average acceleration of the ball in contact with the bat.
2. calculate the magnitude of the average force the bat exerts on the ball while they are in contact.

1. 8000 m/s^2 east

To determine the magnitude and direction of the average acceleration of the ball in contact with the bat, we can use the following formula:

Acceleration = (Final Velocity - Initial Velocity) / Time

1. Initial velocity of the ball = 45 m/s west
2. Final velocity of the ball = 35 m/s
3. Time of contact = 1.0 * 10^-2 seconds

Step 1: Calculating the change in velocity:
Change in velocity = Final Velocity - Initial Velocity
= 35 m/s - (-45 m/s) [keeping in mind that the ball is moving west]

Step 2: Substituting the values into the formula:
Acceleration = Change in velocity / Time
= (35 m/s - (-45 m/s)) / (1.0 * 10^-2 seconds)

Simplifying the expression:
Acceleration = 80 m/s / (1.0 * 10^-2 seconds)

To convert seconds to microseconds, we multiply by 1,000,000:
Acceleration = 80 * 10^6 m/s^2 (direction West)

Therefore, the magnitude of the average acceleration of the ball in contact with the bat is 80 * 10^6 m/s^2, and the direction is west.

Now let's move on to calculating the magnitude of the average force the bat exerts on the ball while they are in contact.

We can use Newton's second law of motion to calculate the force:

Force = Mass * Acceleration

1. Mass of the ball = 0.14 kilograms (given)
2. Acceleration of the ball = 80 * 10^6 m/s^2 (calculated in the previous step)

Step 1: Substituting the values into the formula:
Force = Mass * Acceleration
= 0.14 kilograms * 80 * 10^6 m/s^2

Simplifying the expression:
Force = 11.2 * 10^6 Newtons

Therefore, the magnitude of the average force the bat exerts on the ball while they are in contact is 11.2 * 10^6 Newtons.

To determine the magnitude and direction of the average acceleration of the ball in contact with the bat, we can use the equation for average acceleration:

Average acceleration = (change in velocity) / (time taken)

1. Change in velocity:
The change in velocity of the ball can be calculated by subtracting its initial velocity from its final velocity:

Change in velocity = final velocity - initial velocity
= 35 m/s - (-45 m/s)
= 35 m/s + 45 m/s
= 80 m/s

2. Time taken:
The time taken for the bat and ball to be in contact is given as 1.0 * 10^-2 seconds.

Now, we can calculate the average acceleration:

Average acceleration = (change in velocity) / (time taken)
= 80 m/s / (1.0 * 10^-2 s)
= 8000 m/s^2

Therefore, the magnitude of the average acceleration of the ball in contact with the bat is 8000 m/s^2.

Now, to determine the direction of the average acceleration, we need to consider the initial and final velocities of the ball.

The initial velocity of the ball is given as 45 m/s west, and the final velocity is given as 35 m/s. Since these velocities are in opposite directions, we can infer that the average acceleration vector will be directed towards the east or in the opposite direction of the initial velocity.

So, the direction of the average acceleration of the ball in contact with the bat is east.

Next, we'll calculate the magnitude of the average force the bat exerts on the ball while they are in contact.

3. Magnitude of average force:

Using Newton's second law, F = ma, where F is force, m is mass, and a is acceleration.

The mass of the baseball is given as 0.14 kilograms.

Therefore, the magnitude of the average force can be calculated as:

Force = mass * acceleration
= 0.14 kg * 8000 m/s^2
= 1120 Newtons

Hence, the magnitude of the average force that the bat exerts on the ball while they are in contact is 1120 Newtons.