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.

Open in App
Solution

## Step 1: Given dataMass of the boy is $m=50kg$. The height of each step is $15cm$.The total number of steps is $45$.The total time taken by the boy is $9s$.Step 2: Power and potential energyPower is the energy in unit time, i.e, power, $p=\frac{U}{t}$, where, U is the energy and t is the time.Power is the rate of doing work. The unit of power is watt.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 bodyThe total distance traveled by the boy is $h=0.15×45\phantom{\rule{0ex}{0ex}}h=6.75m.$Now, the energy of the boy at a height $6.75m$is $U=mgh\phantom{\rule{0ex}{0ex}}orU=50×9.8×6.75\phantom{\rule{0ex}{0ex}}orU=3307.5$So, power, $p=\frac{U}{t}=\frac{3307.5}{9}\phantom{\rule{0ex}{0ex}}orp=367.5watt$Therefore, the power of the boy is $367.5watt.$

Suggest Corrections
0