A boy of mass 50 kg runs up a flight of 120 stairs, each measuring a height of 25 cm, in one minute and 40 seconds. If g = 10 m `s^(-2)`, the power of the boy is

Options

A. 150 W
B. 750 W
C. 500 W
D. 250 W

Explanation

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

### Step 1: Calculate the total height climbed
The boy climbs 120 stairs, each with a height of 25 cm.
- Total height (H) = Number of stairs × Height of each stair
- H = 120 stairs × 25 cm/stair = 3000 cm

Now, convert this height into meters:
- H = 3000 cm ÷ 100 = 30 m

### Step 2: Calculate the work done
The work done against gravity when climbing is equal to the potential energy gained, which can be calculated using the formula:
- Work done (W) = m × g × H
Where:
- m = mass of the boy = 50 kg
- g = acceleration due to gravity = 10 m/s²
- H = height climbed = 30 m

Now substituting the values:
- W = 50 kg × 10 m/s² × 30 m = 15000 J (Joules)

### Step 3: Convert time into seconds
The time taken to climb the stairs is given as 1 minute and 40 seconds.
- Convert this into seconds:
- Time (T) = 1 minute × 60 seconds/minute + 40 seconds = 100 seconds

### Step 4: Calculate the power
Power (P) is defined as the work done per unit time:
- P = W / T
Substituting the values we calculated:
- P = 15000 J / 100 s = 150 W (Watts)

### Final Answer
The power of the boy is **150 Watts**.

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