A man carries a load of 50 kg to a height of 40 m is 25s. If the power of the man is 1568 W, the mass of the man is

Options

A. 20 kg
B. 50 kg
C. 100 kg
D. 75 kg

Answer

To solve the problem, we need to find the mass of the man who carries a load of 50 kg to a height of 40 m in 25 seconds, while exerting a power of 1568 W.

### Step-by-Step Solution:

1. **Identify Given Values**:
- Mass of the load (ml) = 50 kg
- Height (h) = 40 m
- Time (t) = 25 s
- Power (P) = 1568 W
- Acceleration due to gravity (g) = 9.8 m/s² (approximately 10 m/s² for simplicity)

2. **Calculate Work Done (W)**:
The work done against gravity when lifting the load is given by the formula:
\[ W = m \cdot g \cdot h \]
where \( m \) is the total mass being lifted (mass of the load + mass of the man).

3. **Express Power in Terms of Work Done**:
Power is defined as work done per unit time:
\[ P = \frac{W}{t} \]
Rearranging gives:
\[ W = P \cdot t \]

4. **Substituting Values**:
Substitute the power and time into the equation:
\[ W = 1568 \, \text{W} \cdot 25 \, \text{s} = 39200 \, \text{J} \]

5. **Setting Up the Equation for Total Mass**:
Now we can set up the equation for work done:
\[ W = (ml + m) \cdot g \cdot h \]
Substituting the values we have:
\[ 39200 = (50 + m) \cdot 9.8 \cdot 40 \]

6. **Simplifying the Equation**:
Calculate \( 9.8 \cdot 40 \):
\[ 9.8 \cdot 40 = 392 \]
Thus, we can rewrite the equation:
\[ 39200 = (50 + m) \cdot 392 \]

7. **Dividing Both Sides by 392**:
\[ 100 = 50 + m \]

8. **Solving for the Mass of the Man (m)**:
\[ m = 100 - 50 = 50 \, \text{kg} \]

### Final Answer:
The mass of the man is **50 kg**.