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 range \( r \) of an antenna is given by the formula:
\[ r = \sqrt{2 \cdot R_e \cdot h_t} \]
where:
- \( R_e \) is the radius of the Earth (approximately \( 6.4 \times 10^6 \) meters),
- \( h_t \) is the height of the antenna (in this case, 20 meters).

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

3. **Calculate the Product Inside the Square Root**:
First, calculate \( 2 \cdot 6.4 \times 10^6 \):
\[ 2 \cdot 6.4 = 12.8 \quad \text{and thus} \quad 12.8 \times 10^6 \]
Now multiply by 20:
\[ 12.8 \times 10^6 \cdot 20 = 256 \times 10^6 \]

4. **Take the Square Root**:
Now take the square root of \( 256 \times 10^6 \):
\[ r = \sqrt{256 \times 10^6} = \sqrt{256} \times \sqrt{10^6} = 16 \times 10^3 \]

5. **Convert to Kilometers**:
Since \( 10^3 \) meters equals 1 kilometer:
\[ r = 16 \times 10^3 \text{ meters} = 16 \text{ kilometers} \]

6. **Final Answer**:
Therefore, the distance of propagation from the antenna of height 20 meters is:
\[ \text{Distance} = 16 \text{ kilometers} \]