A boy of mass 50kg runs up a staricase of 45 steps in 9s. If the height of each step is 15cm, find his power. Take `g = 10m//s^2`

Options

A. `275W`
B. `375W`
C. `475W`
D. `575W`

Explanation

To find the power exerted by the boy while running up the staircase, we can follow these steps:

### Step 1: Calculate the total height climbed
The total height (h) climbed by the boy can be calculated using the formula:
\[ h = \text{number of steps} \times \text{height of each step} \]

Given:
- Number of steps = 45
- Height of each step = 15 cm = 0.15 m (since 1 cm = 0.01 m)

Calculating the total height:
\[ h = 45 \times 0.15 = 6.75 \text{ m} \]

### Step 2: Calculate the work done
The work done (W) against gravity is given by the formula:
\[ W = mgh \]

Where:
- \( m \) = mass of the boy = 50 kg
- \( g \) = acceleration due to gravity = 10 m/s²
- \( h \) = total height climbed = 6.75 m

Calculating the work done:
\[ W = 50 \times 10 \times 6.75 = 3375 \text{ J} \]

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

Where:
- \( W \) = work done = 3375 J
- \( t \) = time taken = 9 s

Calculating the power:
\[ P = \frac{3375}{9} = 375 \text{ W} \]

### Final Answer
The power exerted by the boy while running up the staircase is **375 Watts**.

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