Question

A boy of mass 60 kg runs up a staircase of 60 steps in 1 minute. If the height of

each step is 15 cm, find his power. Take g = 10 m/s² ​

Answer 1

Given :

• Mass of the boy = 60kg
• Number of steps in the staircase = 45
• height of each step = 15cm
• Value of 'g' = 10m/s²
• Time taken = 1 min = 60 seconds

To Find :

• Power of the Boy

Formula Applied :

${\boxed{{\boxed{\sf{p = \frac{mgh}{t}}}}}}$

• ${\sf{p=power }}$
• $\sf{ m =Mass \: of\: the \: body }$
• $\sf{g = acceleration \: due\: to \: gravity }$
• $\sf{h=height}$
• $\sf{t = times\:taken}$

Solution :

• Before substituting the given values in the formula, we have to find the total height climbed by the boy. The total climbed by the boy can be calculated by multiplying number of steps with height of each step.

$\implies \sf{45 \times 15\: cm}$

$\implies \sf{675 \:cm}$

$\implies \sf{6.75 \:m}$

• Now substitute the values in the formula of power of the body.

$\rightarrow \displaystyle {\sf{p = \frac{mgh}{t}}}$

$\displaystyle {\rightarrow \sf{p = \frac{60 \times 10 \times 6.75}{60}}}$

$\rightarrow \sf{p = 10 \times 6.75}$

$\rightarrow \sf{p =67.5 w}$

Required Answer :

The power of the boy is 67.5 w

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Learn More :

• Power of a machine is defined as the rate of work done by a machine. It is a scalar quantity.
• S.I. unit of power is Watt(W). Another unit of power is Horse Power (HP).
• If work done by a machine is 1 Joule in a time of 1 second, then power of the machine is 1 Watt.