Question

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

• A. $19.77m$
• B. $79.1m$
• C. $158.2m$
• D. $39.55m$

Answer 1

The correct option is D

$39.55m$

Step 1: Given;

Suppose the minimum height of the receiving antenna is $h_2$ and the height of the other antenna is $h_1$.

Range, $d=45km$ and $h_1=h_2=h$

Radius of earth, $R=6,400km$

Step 2: Formula used;

Range, $d=2\sqrt{2Rh}$

where $R$ is the radius of the earth and $h$ is the height of receiving antenna.

Step 3: Find the minimum height of the receiving antenna.

Range,

$$\begin{gathered} d=2\sqrt{2Rh} \\ \Rightarrow h=\frac{d^2}{8R}=\frac{{45}^2}{8\times 6400}Km=39.55m \end{gathered}$$

The minimum height of the receiving antenna is $39.55m$.

Hence, option D is correct.