Question

A student of mass 45kg, who is undergoing National Service training, takes 6s to climb a flight of stairs that had 36 steps. If each step is 16cm high, what is the power of the student?

Answer 1

Approximately
`4.2 * 10^(2)\; \rm W` on average in the vertical direction (assuming that
`g = 9.8\; \rm N \cdot kg^(-1)`.)

Step-by-step explanation:

Vertical displacement of this student in
`6\; \rm s`:
`36 * 16\; \rm cm = 36 * (0.16\; \rm m) = 5.76\; \rm m`.

Average vertical velocity of this student:
`v = \displaystyle (5.76\; \rm m)/(6\; \rm s) = 0.96\; \rm m \cdot s^(-1)`.

The average vertical force that this student exerts on the ground would be equal to the weight of this student:

`F = W = m \cdot g = 45\; \rm kg * 9.8\; \rm N \cdot kg^(-1) = 441\; \rm N`.

The average power of this student in the vertical direction is equal to the product of the force and velocity of this student in that direction:

`P = F \cdot v = 441\; \rm N * 0.96\; \rm m \cdot s^(-1) \approx 4.2* 10^(2)\; \rm W`.