Question

A 40 kg student runs up stairs to a floor that is 5 meters higher than her starting point in 7 seconds. What is the student's power output?

1) 14,000 W
2) 280 W
3) 140,000 W
4) 29 W

Answer 1

The student's power output while running up the stairs is calculated using the formula: Power (P) = Work done (W) / Time taken (t). The work done is derived from the potential energy change as W = mgh. Then, by substituting the given values, the power output is found to be 280 watts. Therefore, the correct option is 2.

Step-by-step explanation:

To calculate the student's power output, we need to use the formula for power related to work and time: Power (P) = Work done (W) / Time taken (t). Work done is equal to the change in potential energy, which is given by W = mgh, where m is mass, g is the acceleration due to gravity, and h is the height.

The student's mass (m) is 40 kg, the acceleration due to gravity (g) is approximately 9.8 m/s², and the height of the stairs (h) is 5 meters. The time taken (t) to climb the stairs is 7 seconds.

First, calculate the work done: W = mgh = (40 kg)(9.8 m/s²)(5 m) = 1960 J.

Then, calculate the power output: P = W / t = 1960 J / 7 s = 280 W.

Therefore, the student's power output is 280 watts.