Weight of a person is 800 N. If he runs 4 m on a vertical ladder in 2s then he needs a power of

Options

A. 3200 kW
B. 3.2 kW
C. 1.6 kW
D. zero

Answer

To solve the problem step by step, we will calculate the power required by the person to run up a vertical ladder.

### Step 1: Understand the Problem
The weight of the person is given as 800 N, and he runs up a vertical ladder with a height of 4 m in 2 seconds. We need to find the power he requires to do this.

### Step 2: Identify the Forces
The force that the person needs to overcome while climbing is equal to his weight, which is 800 N. This is because he needs to exert a force equal to his weight to move upward against gravity.

### Step 3: Calculate Work Done
The work done (W) against gravity can be calculated using the formula:
\[ W = \text{Force} \times \text{Displacement} \]
Here, the force is 800 N, and the displacement is 4 m (the height climbed).
\[ W = 800 \, \text{N} \times 4 \, \text{m} = 3200 \, \text{J} \]

### Step 4: Calculate Power
Power (P) is defined as the work done per unit time. The formula for power is:
\[ P = \frac{W}{T} \]
where \( W \) is the work done and \( T \) is the time taken. The time taken is given as 2 seconds.
\[ P = \frac{3200 \, \text{J}}{2 \, \text{s}} = 1600 \, \text{W} \]

### Step 5: Convert Power to Kilowatts
Since power is often expressed in kilowatts (kW), we convert watts to kilowatts:
\[ P = \frac{1600 \, \text{W}}{1000} = 1.6 \, \text{kW} \]

### Final Answer
The power needed by the person is **1.6 kW**.

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