A man weighing 60 kg climbs up a staircase carrying a load of 20 kg on his head. The staircase has 20 steps each of height 0.2 m. If he takes 10 s to climb, find his power.

Options

A. 313.6 W
B. 120.6 W
C. 510 W
D. 0

Explanation

To find the power exerted by the man while climbing the staircase, we can follow these steps:

### Step 1: Calculate the Total Weight
The total weight the man is carrying consists of his own weight and the weight of the load on his head.

- Weight of the man = 60 kg
- Weight of the load = 20 kg

Total weight (W) = Weight of the man + Weight of the load
W = 60 kg + 20 kg = 80 kg

### Step 2: Calculate the Height Climbed
The height of each step is given as 0.2 m, and there are 20 steps.

Height climbed (h) = Number of steps × Height of each step
h = 20 steps × 0.2 m/step = 4 m

### Step 3: Calculate the Work Done
The work done (W_d) against gravity is given by the formula:

\[ W_d = \text{Total weight} \times \text{Height climbed} \times g \]

Where \( g \) (acceleration due to gravity) is approximately \( 9.81 \, \text{m/s}^2 \).

So,
\[ W_d = 80 \, \text{kg} \times 4 \, \text{m} \times 9.81 \, \text{m/s}^2 \]
\[ W_d = 80 \times 4 \times 9.81 = 3130.4 \, \text{J} \]

### Step 4: Calculate the Power
Power (P) is defined as the work done per unit time. The time taken to climb the stairs is given as 10 seconds.

\[ P = \frac{W_d}{t} \]

Where \( t \) is the time taken.

So,
\[ P = \frac{3130.4 \, \text{J}}{10 \, \text{s}} \]
\[ P = 313.04 \, \text{W} \]

### Final Answer
The power exerted by the man while climbing the staircase is approximately **313.04 Watts**.

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