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 distance of propagation (D) from a height (H) above the Earth's surface. The formula is given by:

\[ D = \sqrt{2 \cdot H \cdot R} \]

where:
- \( D \) is the distance of propagation,
- \( H \) is the height of the antenna,
- \( R \) is the radius of the Earth (approximately \( 6.4 \times 10^6 \) meters).

### Step-by-Step Solution:

1. **Identify the given values:**
- Height of the antenna, \( H = 20 \) meters
- Radius of the Earth, \( R = 6.4 \times 10^6 \) meters

2. **Substitute the values into the formula:**
\[ D = \sqrt{2 \cdot H \cdot R} \]
\[ D = \sqrt{2 \cdot 20 \cdot (6.4 \times 10^6)} \]

3. **Calculate the product inside the square root:**
\[ 2 \cdot 20 = 40 \]
\[ 40 \cdot (6.4 \times 10^6) = 256 \times 10^6 \]

4. **Take the square root:**
\[ D = \sqrt{256 \times 10^6} = \sqrt{256} \times \sqrt{10^6} \]
\[ D = 16 \times 10^3 = 16000 \text{ meters} \]

5. **Convert meters to kilometers:**
\[ D = 16000 \text{ meters} = 16 \text{ kilometers} \]

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