Final answer:
The power output of the sprinter is 1167 watts and 1.57 horsepower. A well-trained athlete may not be able to do this repetitively for long periods of time.
Step-by-step explanation:
To find the power output of the sprinter, we can use the equation:
Power = (Work done) / (Time taken)
First, let's calculate the work done. We know that work is equal to the change in kinetic energy, so:
Work = (1/2) * mass * (final velocity^2 - initial velocity^2)
Plugging in the values:
Work = (1/2) * 70.0 kg * (10.0 m/s)^2 - 0
Work = 3500 J
Next, we can calculate the power using the formula:
Power = Work / Time
Plugging in the values:
Power = 3500 J / 3.00 s
Power = 1167 W
To convert the power to horsepower, we can use the conversion factor 1 hp = 746 W:
Power(hp) = Power(W) / 746
Plugging in the values:
Power(hp) = 1167 W / 746
Power(hp) = 1.57 hp
So, the power output of the sprinter is 1167 watts and 1.57 horsepower.
As for whether a well-trained athlete could do this repetitively for long periods of time, it would depend on their training and stamina. Sprinting at full power continuously for a long period of time would be challenging and potentially unsustainable.
Answer: (a) 1167 W, 1.57 hp, (b) No