A body of mass 1 kg is thrown upwards with a velocity 20 m/s. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction `(g = 10 m//s^2)`

Options

A. 20 J
B. 30 J
C. 40 J
D. 10 J

Explanation

To solve the problem of how much energy is lost due to air friction when a body of mass 1 kg is thrown upwards with a velocity of 20 m/s and reaches a height of 18 m, we can follow these steps:

### Step 1: Calculate the Initial Kinetic Energy (KE_initial)
The initial kinetic energy of the body can be calculated using the formula:
\[ KE_{\text{initial}} = \frac{1}{2} m u^2 \]
where:
- \( m = 1 \, \text{kg} \) (mass of the body)
- \( u = 20 \, \text{m/s} \) (initial velocity)

Substituting the values:
\[ KE_{\text{initial}} = \frac{1}{2} \times 1 \times (20)^2 = \frac{1}{2} \times 1 \times 400 = 200 \, \text{J} \]

### Step 2: Calculate the Potential Energy (PE) at Maximum Height
The potential energy at the maximum height can be calculated using the formula:
\[ PE = mgh \]
where:
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( h = 18 \, \text{m} \) (maximum height reached)

Substituting the values:
\[ PE = 1 \times 10 \times 18 = 180 \, \text{J} \]

### Step 3: Calculate the Energy Lost Due to Air Friction
The energy lost due to air friction can be found by comparing the initial kinetic energy and the potential energy at the maximum height:
\[ \text{Energy lost} = KE_{\text{initial}} - PE \]
Substituting the values:
\[ \text{Energy lost} = 200 \, \text{J} - 180 \, \text{J} = 20 \, \text{J} \]

### Conclusion
The energy lost due to air friction is **20 Joules**.

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