Question

Two identical antennas mounted on identical towers are separated from each other by a distance of $45\text{km}$. What should nearly be the minimum height of receiving antenna to receive the signals in line of sight? (Assume radius of earth is $6400\text{km}$)

• A. $19.77\text{m}$
• B. $79.1\text{m}$
• C. $158.2\text{m}$
• D. $39.55\text{m}$

Answer 1

The correct option is D $39.55\text{m}$

Suppose minimum height of the receiving anteena is $h_2$.

Given, Range, $d=45\text{km}$ and $h_1=h_2=h$

Now, Range$=\sqrt{2Rh}+\sqrt{2Rh}$

$\Rightarrow d=2\sqrt{2Rh}$
$\Rightarrow h=\frac{d^2}{8R}=\frac{{45}^2}{8\times 6400}\text{km}$
$\therefore h=39.55\text{m}$