A man carries a load of `50 kg` through a height of `40 m` in `25` seconds. If the power of the man is `1568 W`, his mass is

Options

A. 5 kg
B. 1000 kg
C. 200 kg
D. 50 kg

Explanation

To find the mass of the man carrying a load, we can use the relationship between power, work done, and time. Here’s a step-by-step solution:

### Step 1: Understand the formula for power
Power (P) is defined as the work done (W) per unit time (t):
\[ P = \frac{W}{t} \]

### Step 2: Calculate the work done against gravity
The work done in lifting a load to a height \( h \) is given by:
\[ W = mgh \]
where:
- \( m \) is the total mass (mass of the man + mass of the load)
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \))
- \( h \) is the height (40 m in this case)

### Step 3: Substitute the work done into the power formula
We can substitute the expression for work done into the power formula:
\[ P = \frac{mgh}{t} \]
Rearranging gives us:
\[ m = \frac{Pt}{gh} \]

### Step 4: Substitute known values
We know:
- \( P = 1568 \, \text{W} \)
- \( t = 25 \, \text{s} \)
- \( g = 9.8 \, \text{m/s}^2 \)
- \( h = 40 \, \text{m} \)

The total mass \( m \) is the mass of the man \( M \) plus the mass of the load (50 kg):
\[ m = M + 50 \]

### Step 5: Set up the equation
Substituting into the rearranged power formula:
\[ M + 50 = \frac{1568 \times 25}{9.8 \times 40} \]

### Step 6: Calculate the right side
Calculating the right side:
\[ M + 50 = \frac{39200}{392} = 100 \]

### Step 7: Solve for the mass of the man
Now, we can solve for \( M \):
\[ M = 100 - 50 = 50 \, \text{kg} \]

### Final Answer
The mass of the man is \( 50 \, \text{kg} \).

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