Question

A boy of mass 50 kg runs up a stair case of 45 steps in 9s. If the height of each step is 15 cm, find his power.

(Take g = 10 ms^-2)

Answer 1

Step 1: Given Data

1. Mass (m) = 50 kg
2. Height of 1 step = 15 cm
3. Number of steps = 45
4. Time (t) = 9 s

Step 2: Formula used

1. Power(P) = Energy(E)/Time(t)
2. Energy(E) = mass(m) x acceleration due to gravity(g) x height(h)

Step 3: Converting the given height of 1 step to the base unit,

1 m = 100 cm

So, 15 cm = $\frac{15}{100}$ = 0.15 m

Step 4: Finding the total height

Total height (h) = height of 1 step x number of steps

h = 0.15 m x 45

h = 6.75 m

Step 5: Finding the value of energy

Energy = mgh

E = 50 x 10 x 6.75

E = 3375 J

Step 6: Finding power

P = E/t

P = $\frac{3375}{9}$

P = 375 W

Hence, the power of the boy is 375 W.