Question

A boy of mass $50\,{\text{kg}}$ runs up a staircase of ${\text{45}}$ steps in ${\text{9 s}}$. If the height of each step is ${\text{15 cm}}$, find his power. Take $g = 10\,{\text{m}}{{\text{s}}^{{\text{ - 2}}}}$.

Answer 1

Write down the given values. We are asked to find the value of power the boy has used to run up to $45$ steps in $9\,{\text{s}}$. For, this first recall the formula for power, check what are the quantities required to find the value of power. From the given quantities, find out the values of required quantities to calculate the value of boy’s power.

Complete step by step answer:
Given, mass of the boy, $m = 50\,{\text{kg}}$
No of steps, $n = 45$
Height of each step, $h = 15\,{\text{cm}}$
Time taken, $t = 9\,{\text{s}}$
Gravitational acceleration, $g = 10\,{\text{m}}{{\text{s}}^{{\text{ - 2}}}}$

We are asked to find the power of the boy, we have the formula for power as,
$P = \dfrac{{{\text{Energy}}}}{{{\text{Time}}}}$
So, to find out the value of power, we must first know the value of the boy’s energy
Potential energy of the boy can be written as,
$P.E = mgH$ (i)
where $m$ is the mass of the boy, $g$ is the acceleration due to gravity and $H$ is the total height the boy runs.

Total height will be,
$H = nh$
Putting the values of $n$ and $h$ we have,

\Rightarrow H = 675\,\,{\text{cm}} \\\ \Rightarrow H = 6.75\,{\text{m}} $$ Now, putting the values of $$m$$,$$g$$ and $$H$$ in equation (i), we get the value for potential energy as $$P.E = 50 \times 10 \times 6.75 \\\ \Rightarrow P.E = 3375\,{\text{J}} $$ Now, power of the boy will be, $$P = \dfrac{{P.E}}{{{\text{Time taken}}}}$$ Putting the values of potential energy and time, we get $$P = \dfrac{{3375}}{9} \\\ \therefore P = 375\,{\text{Watt}} $$ **Therefore, the power of the boy will be $$375\,{\text{Watt}}$$.** **Note:** Always remember when you are required to find the value potential energy of a body of mass $$m$$ at a height say $$h$$, use the formula $$mgh$$. The value of $$g$$ or acceleration due to gravity is usually given in the question but if it is not given take the value of $$g$$ as $$10\,{\text{m}}{{\text{s}}^{{\text{ - 2}}}}$$. Taking the value of $$g$$ as $$10\,{\text{m}}{{\text{s}}^{{\text{ - 2}}}}$$ instead of $$9.8\,{\text{m}}{{\text{s}}^{{\text{ - 2}}}}$$ will make your calculations easy.