A machine makes a man weighing 60 kg move with high velocity of 30 m/s the total mechanical energy of the man if he at a height of 50 m at this speed is

Options

A. 23Kj
B. 57 KJ
C. 94 KJ
D. 106 KJ

Answer

To find the total mechanical energy of the man, we need to calculate both his kinetic energy (KE) and potential energy (PE) at the given height and speed.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the man, \( m = 60 \, \text{kg} \)
- Velocity of the man, \( v = 30 \, \text{m/s} \)
- Height above the ground, \( h = 50 \, \text{m} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \) (assuming standard value)

2. **Calculate Kinetic Energy (KE):**
The formula for kinetic energy is:
\[ KE = \frac{1}{2} mv^2 \]
Substituting the known values:
\[ KE = \frac{1}{2} \times 60 \, \text{kg} \times (30 \, \text{m/s})^2 \]
\[ KE = \frac{1}{2} \times 60 \times 900 \]
\[ KE = 30 \times 900 = 27000 \, \text{J} = 27 \, \text{kJ} \]

3. **Calculate Potential Energy (PE):**
The formula for potential energy is:
\[ PE = mgh \]
Substituting the known values:
\[ PE = 60 \, \text{kg} \times 10 \, \text{m/s}^2 \times 50 \, \text{m} \]
\[ PE = 60 \times 10 \times 50 \]
\[ PE = 30000 \, \text{J} = 30 \, \text{kJ} \]

4. **Calculate Total Mechanical Energy (TME):**
The total mechanical energy is the sum of kinetic energy and potential energy:
\[ TME = KE + PE \]
\[ TME = 27 \, \text{kJ} + 30 \, \text{kJ} \]
\[ TME = 57 \, \text{kJ} \]

### Final Answer:
The total mechanical energy of the man is \( 57 \, \text{kJ} \).

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