A 40 kg girl runs up a flight of stairs having a rise of 5 m in 4 s. The power developed by her will be _____(take `g= 10 m//s^(2)`)

Options

A. 100 W
B. 200 W
C. 500 W
D. 2000 W

Answer

To solve the problem of finding the power developed by the girl running up the stairs, we can follow these steps:

### Step 1: Identify the given values
- Mass of the girl (m) = 40 kg
- Height of the stairs (h) = 5 m
- Time taken (t) = 4 s
- Acceleration due to gravity (g) = 10 m/s²

### Step 2: Calculate the work done (W)
The work done against gravity when the girl runs up the stairs can be calculated using the formula:
\[ W = m \cdot g \cdot h \]

Substituting the values:
\[ W = 40 \, \text{kg} \times 10 \, \text{m/s}^2 \times 5 \, \text{m} \]
\[ W = 40 \times 10 \times 5 \]
\[ W = 2000 \, \text{J} \] (Joules)

### Step 3: Calculate the power (P)
Power is defined as the work done per unit time. The formula for power is:
\[ P = \frac{W}{t} \]

Substituting the values:
\[ P = \frac{2000 \, \text{J}}{4 \, \text{s}} \]
\[ P = 500 \, \text{W} \] (Watts)

### Final Answer
The power developed by the girl is **500 Watts**.

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