If the heights of transmitting and the receiving antennas are each equal to h, the maximum line-of-sight distance between them is (R is the radius of earth)

Options

A. `sqrt(2Rh)`
B. `sqrt(4Rh) `
C. `sqrt(6 Rh) `
D. `sqrt(8 Rh) `

Explanation

To find the maximum line-of-sight distance between two antennas of equal height \( h \), we can use the following steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the maximum line-of-sight distance \( d_m \) between two antennas, both at height \( h \) above the Earth's surface. The radius of the Earth is denoted as \( R \).

2. **Use the Formula for Line-of-Sight Distance**: The formula for the maximum line-of-sight distance between two antennas is given by:
\[ d_m = \sqrt{2Rh_1} + \sqrt{2Rh_2} \]
where \( h_1 \) and \( h_2 \) are the heights of the transmitting and receiving antennas, respectively.

3. **Substitute the Heights**: Since both antennas are at the same height \( h \), we can substitute \( h_1 = h \) and \( h_2 = h \) into the formula:
\[ d_m = \sqrt{2Rh} + \sqrt{2Rh} \]

4. **Combine the Terms**: Since both terms are identical, we can combine them:
\[ d_m = 2\sqrt{2Rh} \]

5. **Simplify the Expression**: We can rewrite \( 2\sqrt{2Rh} \) in a different form:
\[ d_m = \sqrt{8Rh} \]

6. **Final Result**: Thus, the maximum line-of-sight distance \( d_m \) between the two antennas is:
\[ d_m = \sqrt{8Rh} \]