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 find the power required by the person running up the ladder.

### Step 1: Understand the concept of power
Power is defined as the rate at which work is done. Mathematically, it can be expressed as:
\[ P = \frac{dW}{dt} \]
where \( P \) is power, \( dW \) is the work done, and \( dt \) is the time taken.

### Step 2: Relate work done to force and displacement
The work done \( dW \) can also be expressed in terms of force \( F \) and displacement \( dS \):
\[ dW = F \cdot dS \]
Thus, power can be rewritten as:
\[ P = \frac{F \cdot dS}{dt} \]

### Step 3: Recognize that \( \frac{dS}{dt} \) is velocity
Since \( \frac{dS}{dt} \) is the velocity \( v \), we can rewrite the power equation as:
\[ P = F \cdot v \]

### Step 4: Identify the given values
From the problem, we know:
- Weight of the person (force due to gravity) \( F = 800 \, \text{N} \)
- Distance traveled \( dS = 4 \, \text{m} \)
- Time taken \( dt = 2 \, \text{s} \)

### Step 5: Calculate the velocity
To find the velocity \( v \), we use the formula:
\[ v = \frac{dS}{dt} \]
Substituting the values:
\[ v = \frac{4 \, \text{m}}{2 \, \text{s}} = 2 \, \text{m/s} \]

### Step 6: Calculate the power
Now, substitute the values of force and velocity into the power equation:
\[ P = F \cdot v = 800 \, \text{N} \cdot 2 \, \text{m/s} \]
\[ P = 1600 \, \text{W} \]

### Step 7: Convert power to kilowatts
To express the power in kilowatts:
\[ P = \frac{1600 \, \text{W}}{1000} = 1.6 \, \text{kW} \]

### Final Answer
The power required by the person is \( 1.6 \, \text{kW} \).

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