Kenya finally loses her cool and punches her teacher. The teacher weighs 85 kg. He sees the punch coming and begins to back up at a speed of 0.60 m/s. After Kenya clocks him, he is moving backwards at a speed of 0.82 m/s. If the contact time of Kenya's fist to the teachers nose was 0.075 s, what average force did her punch have?

To find the average force of Kenya's punch, we can use the impulse-momentum principle. The impulse is defined as the change in momentum, and in this case, the impulse is equal to the force multiplied by the time of contact. Therefore, we can use the equation:

Impulse = Force × Time

The initial momentum of the teacher before being punched can be calculated using:

Initial Momentum = Mass × Initial Velocity

The final momentum of the teacher after being punched can be calculated using:

Final Momentum = Mass × Final Velocity

Since the magnitude of momentum is conserved, the change in momentum (impulse) is equal to the final momentum minus the initial momentum:

Impulse = Final Momentum - Initial Momentum

Finally, dividing the impulse by the time of contact will give us the average force:

Average Force = Impulse ÷ Time

Now, let's calculate the average force:

1. Calculate the initial momentum:
Initial Momentum = Mass × Initial Velocity

Given:
Teacher's weight = 85 kg
Initial velocity of the teacher = 0.60 m/s

Initial Momentum = 85 kg × 0.60 m/s

2. Calculate the final momentum:
Final Momentum = Mass × Final Velocity

Given:
Final velocity of the teacher = 0.82 m/s

Final Momentum = 85 kg × 0.82 m/s

3. Calculate the impulse:
Impulse = Final Momentum - Initial Momentum

4. Calculate the average force:
Average Force = Impulse ÷ Time

Given:
Time of contact = 0.075 s

Now, plug in the values and calculate the average force.