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Chapter 6: Problem 38

A 75 -kg long-jumper takes 3.1 s to reach a prejump speed of \(10 \mathrm{m} / \mathrm{s} .\) What's his power output?

Short Answer

Expert verified
The power output of the long-jumper is 1209.68 W.

Step by step solution

01

Calculate the kinetic energy

First calculate the change in kinetic energy of the long-jumper using the formula \(1/2* m * v^2\), where m is the mass and v is the velocity. Given, m=75kg, v=10m/s, the kinetic energy would be \(1/2 * 75 kg * (10 m/s)^2 = 3750 J (Joules)\).
02

Calculate the power output

Next, calculate the power output. Power is defined as work done per unit of time. Since the work done here is equivalent to the kinetic energy gained, the power output can be calculated by dividing the kinetic energy by the time taken to achieve this energy. Given, time (t)= 3.1s, power (P) would be \(3750 J / 3.1 s = 1209.68 W (Watts)\).

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