Question

In a line of sight radio communication, a distance of about $50\text{km}$ is kept between the transmitting and receiving antennas. If the height of the receiving antenna is $70\text{m}$, then the minimum height of the transmitting antenna should be:
(Radius of the Earth $=6.4\times {10}^6\text{m}$).

• A. $40\text{m}$
• B. $51\text{m}$
• C. $20\text{m}$
• D. $32\text{m}$

Answer 1

The correct option is D $32\text{m}$

The maximum line of sight of both the antennas is,

LOS $=\sqrt{2h_{T}R}+\sqrt{2h_{R}R}$

$50\times {10}^3=\sqrt{2\times h_T\times 6.4\times {10}^6}+\sqrt{2\times 70\times 6.4\times {10}^6}$

On solving, we get, $h_T=32\text{m}$

Hence, $\left(C\right)$ is the correct answer.