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

Options

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

Answer

To solve the problem, we will use the principle of conservation of energy. The total mechanical energy of the body when it is thrown upwards is converted into potential energy at the maximum height it reaches. However, some energy is lost due to air friction.

### Step 1: Calculate the initial kinetic energy (KE_initial)
The initial kinetic energy when the body is thrown upwards can be calculated using the formula:
\[ KE_{\text{initial}} = \frac{1}{2} m v^2 \]
Where:
- \( m = 1 \, \text{kg} \) (mass of the body)
- \( v = 20 \, \text{m/s} \) (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 final potential energy (PE_final)
The potential energy at the maximum height can be calculated using the formula:
\[ PE_{\text{final}} = mgh \]
Where:
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( h = 18 \, \text{m} \) (maximum height)

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

### Step 3: Calculate the energy lost due to air friction
The energy lost due to air friction can be found by taking the difference between the initial kinetic energy and the final potential energy:
\[ \text{Energy lost} = KE_{\text{initial}} - PE_{\text{final}} \]
Substituting the values we calculated:
\[ \text{Energy lost} = 200 \, \text{J} - 180 \, \text{J} = 20 \, \text{J} \]

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

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