Question

A boy of mass 50 kg, runs up a flight of 120 stairs, each measuring 25 cm in one minute and 40 seconds. If g = 10 ms^-2, the power of the boy is

• A. 150 W
• B. 750 W
• C. 500 W
• D. 250 W

Answer 1

The correct option is A

150 W

Step 1: Given data:

Mass of the boy, m = 50 kg,

Acceleration due to gravity, g = 10 ms^-2,

Number of stairs is n = 120,

Height of each stair is h = 25 cm = 0.25 m,

Time duration, t = 1 min and 40 sec = 100 sec, and

To find, the work done by the boy, W

Step 2: Formula used
Total height = height of each stair x total number of stairs

H = h x n

where H is the total height climbed by a boy.

Substituting the known values,

H = 0.25 m x 120

H = 30 m

Finding the work done by the boy

The work done by the boy is equivalent to the potential energy at the top position.

W = m x g x H

where W is the work done.

Substituting the known values,

W = 50 kg x 10 ms^-2 x 30 m

W = 15000 J

Finding the power of the boy:

$\mathrm{Power}=\frac{\mathrm{Work}\mathrm{done}}{\mathrm{Time}}$

P = $\frac{\mathrm{W}}{\mathrm{t}}$

where P is the power.

Substituting the known values,

$\mathrm{P}=\frac{15000\mathrm{J}}{100\sec }=150\mathrm{J}/\mathrm{s}$

P = 150 W

Step 3: Final answer

Thus, the power of this boy is 150 W.

Hence, option (A) is correct.