A boy of mass 50kg, runs up a staircase of 45 steps in 10s. If the height of each step is 14cm, find his power. Take `"g=10ms"^(-2)`

Options

A. 315ms
B. 315W
C. 337.5W
D. 310.55J

Answer

To find the power of the boy running up the staircase, we can follow these steps:

### Step 1: Calculate the total height of the staircase
The height of each step is given as 14 cm, and there are 45 steps.

\[ \text{Total height} (H) = \text{Number of steps} \times \text{Height of each step} \]
\[ H = 45 \text{ steps} \times 14 \text{ cm/step} = 630 \text{ cm} \]

### Step 2: Convert the height from centimeters to meters
Since 1 meter = 100 centimeters, we need to convert the height into meters:

\[ H = \frac{630 \text{ cm}}{100} = 6.3 \text{ m} \]

### Step 3: Calculate the potential energy (PE)
The formula for potential energy is given by:

\[ PE = m \cdot g \cdot H \]

Where:
- \( m = 50 \text{ kg} \) (mass of the boy)
- \( g = 10 \text{ m/s}^2 \) (acceleration due to gravity)
- \( H = 6.3 \text{ m} \) (height calculated in Step 2)

Substituting the values:

\[ PE = 50 \text{ kg} \cdot 10 \text{ m/s}^2 \cdot 6.3 \text{ m} = 3150 \text{ J} \]

### Step 4: Calculate the power
Power is defined as the rate of doing work or the rate of energy transfer. It can be calculated using the formula:

\[ \text{Power} (P) = \frac{\text{Potential Energy}}{\text{Time}} \]

Given that the time taken is 10 seconds:

\[ P = \frac{3150 \text{ J}}{10 \text{ s}} = 315 \text{ W} \]

### Final Answer
The power of the boy is **315 Watts**.

---