A sprinter mass 72 kg runs the 50 meter dash in 8.35 s. Assume that the sprinter accelerates in the first second and runs the rest of the race at a constant velocity.

(a) Calculate the average power produced for that first second.
1 W
(b) What is the maximum power the sprinter now generates?
2 W

To calculate the average power produced by the sprinter for the first second, we need to use the formula:

Average power = Work / Time

In this case, the work done by the sprinter can be calculated using the formula:

Work = Force * Distance

Now, the force can be calculated using Newton's second law:

Force = Mass * Acceleration

Since the sprinter accelerates in the first second, we need to calculate the acceleration first. We can use the formula:

Acceleration = Change in velocity / Time

The initial velocity of the sprinter is 0 m/s since they start from rest. The final velocity can be calculated using the formula:

Final velocity = Initial velocity + (Acceleration * Time)

Given that the sprinter runs the 50-meter dash in 8.35 seconds, we know that the final velocity is the constant velocity after the first second.

Let's break down the steps to calculate the average power for the first second:

Step 1: Calculate the acceleration
Acceleration = Change in velocity / Time
Change in velocity = Final velocity - Initial velocity
= (50 m / 8.35 s) - 0 m/s
= 5.99 m/s² (rounding to two decimal places)

Step 2: Calculate the force
Force = Mass * Acceleration
= 72 kg * 5.99 m/s²
= 431.28 N (rounding to two decimal places)

Step 3: Calculate the work
Work = Force * Distance
= 431.28 N * 50 m
= 21,564 J (rounding to the nearest whole number)

Step 4: Calculate the average power
Average power = Work / Time
= 21,564 J / 1 s
= 21,564 W

Therefore, the average power produced by the sprinter for the first second is 21,564 W.

Now, let's calculate the maximum power the sprinter generates.

The maximum power a sprinter can generate is when they reach their maximum speed and maintain it until the end. So, we need to calculate the maximum speed reached by the sprinter.

Step 1: Calculate the acceleration during the first second
Acceleration = Change in velocity / Time
Change in velocity = Final velocity - Initial velocity
= (50 m / 1 s) - 0 m/s
= 50 m/s

Step 2: Calculate the maximum speed
Maximum speed = Final velocity + (Acceleration * Time)
= 50 m/s + (0 m/s² * 8.35 s)
= 50 m/s

Now, we can calculate the maximum power using the formula:

Maximum power = Force * Maximum speed

Step 3: Calculate the force
Force = Mass * Acceleration
= 72 kg * 0 m/s²
= 0 N

Step 4: Calculate the maximum power
Maximum power = Force * Maximum speed
= 0 N * 50 m/s
= 0 W

Therefore, the maximum power the sprinter generates is 0 W.