A girl with 50 kg mass climbs up a rope through a height of 5 metres. She takes 25 s to accomplish the task. What is the power (in watts) expended by the girl?
Show answer & explanation
Correct answer: B
Explanation
Given data:
Mass of the girl (m) = 50 kg.
Height (h) = 5 m
Time (t) = 25 sec.
Acceleration due to gravity (g) = 9.8 m/s2 (standard value)
Calculation:
Work done (W): When someone climbs up, the work done is equal to the potential energy against gravity.
\begin{align*} W &= m \cdot g \cdot h \\[10pt] W &= 50 \times 9.8 \times 5 \\[10pt] W &= 2450 \text{ J} \end{align*}
Power (P): The rate of doing work is called power.
\begin{align*} P &= \frac{W}{t} \\[10pt] P &= \frac{2450}{25} \\[10pt] P &= 98 \text{ W} \end{align*}