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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.


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Solution

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=Ut, 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

h=0.15×45h=6.75m.

Now, the energy of the boy at a height 6.75mis

U=mghorU=50×9.8×6.75orU=3307.5

So, power,

p=Ut=3307.59orp=367.5watt

Therefore, the power of the boy is 367.5watt.


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