Question

A boy of mass 50 kg runs up a staircase of 45 steps in 9 s. If the height of each step of the staircase is 15 cm, find the power of the boy.

Answer 1

Step 1: Given data

1. Mass of the boy is $m=50kg$.
2. The height of each step is $15cm$.
3. The total number of steps is $45$.
4. The total time taken by the boy is $9s$.

Step 2: Power and potential energy

1. Power is the energy in unit time, i.e, power, $p=\frac{U}{t}$, where, U is the energy and t is the time.
2. Power is the rate of doing work. The unit of power is watt.
3. We know that the gravitational potential energy of a body of mass m at a height h is defined by the form, $U=mgh$, where U is the gravitational potential energy, and g is the acceleration due to gravity.

Step 3: Find the power of the body

The total distance traveled by the boy is

$$\begin{gathered} h=0.15\times 45 \\ h=6.75m. \end{gathered}$$

Now, the energy of the boy at a height $6.75m$is

$$\begin{gathered} U=mgh \\ orU=50\times 9.8\times 6.75 \\ orU=3307.5 \end{gathered}$$

So, power,

$$\begin{gathered} p=\frac{U}{t}=\frac{3307.5}{9} \\ orp=367.5watt \end{gathered}$$

Therefore, the power of the boy is $367.5watt.$