Distance of propogation from antenna of height 20m is

Options

A. 80km
B. 8km
C. 16km
D. 6.8km

Answer

To find the distance of propagation from an antenna of height 20 meters, we can use the formula for the range of an antenna:

### Step-by-Step Solution:

1. **Identify the Formula**:
The distance of propagation (or range) from an antenna can be calculated using the formula:
\[ d = \sqrt{2 \cdot r_e \cdot h_t} \]
where:
- \( d \) is the distance of propagation,
- \( r_e \) is the radius of the Earth (approximately \( 6.4 \times 10^6 \) meters),
- \( h_t \) is the height of the antenna.

2. **Substitute the Known Values**:
Given:
- Height of the antenna, \( h_t = 20 \) meters,
- Radius of the Earth, \( r_e = 6.4 \times 10^6 \) meters.

Substitute these values into the formula:
\[ d = \sqrt{2 \cdot (6.4 \times 10^6) \cdot 20} \]

3. **Calculate the Product Inside the Square Root**:
First, calculate \( 2 \cdot 6.4 \times 10^6 \):
\[ 2 \cdot 6.4 \times 10^6 = 12.8 \times 10^6 \]
Now multiply by the height of the antenna:
\[ 12.8 \times 10^6 \cdot 20 = 256 \times 10^6 \]

4. **Take the Square Root**:
Now, we take the square root of \( 256 \times 10^6 \):
\[ d = \sqrt{256 \times 10^6} = \sqrt{256} \cdot \sqrt{10^6} = 16 \cdot 10^3 = 16000 \text{ meters} \]

5. **Convert to Kilometers**:
Since \( 1 \text{ kilometer} = 1000 \text{ meters} \):
\[ d = \frac{16000}{1000} = 16 \text{ kilometers} \]

### Final Answer:
The distance of propagation from the antenna of height 20 meters is **16 kilometers**.

---