A 51-kg woman runs up a flight of stairs in 5.0 s. Her net upward displcement is 5.0 m. Approximately, what everage power did the woman exert while she was running ?

Options

A. 5.0W
B. 0.75kW
C. 0.25kW
D. 0.50kW

Answer

To find the average power exerted by the woman while running up the stairs, we can follow these steps:

### Step 1: Calculate the Work Done Against Gravity
The work done (W) against gravity when the woman climbs a height (h) can be calculated using the formula:
\[ W = mgh \]
where:
- \( m = 51 \, \text{kg} \) (mass of the woman),
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity, approximated),
- \( h = 5 \, \text{m} \) (height climbed).

Substituting the values:
\[ W = 51 \, \text{kg} \times 10 \, \text{m/s}^2 \times 5 \, \text{m} \]
\[ W = 51 \times 10 \times 5 = 2550 \, \text{J} \]

### Step 2: Calculate the Average Power
Power (P) is defined as the work done per unit time. The formula for average power is:
\[ P = \frac{W}{t} \]
where:
- \( W = 2550 \, \text{J} \) (work done),
- \( t = 5 \, \text{s} \) (time taken).

Substituting the values:
\[ P = \frac{2550 \, \text{J}}{5 \, \text{s}} \]
\[ P = 510 \, \text{W} \]

### Step 3: Convert Power to Kilowatts
To express the power in kilowatts:
\[ P = \frac{510 \, \text{W}}{1000} = 0.51 \, \text{kW} \]

### Final Answer
The average power exerted by the woman while running up the stairs is approximately **0.51 kW**.

---