Question

A transmitting antenna of height 20 m and the receiving antenna of height h are separated by a distance of 40 km for satisfactory communication in line-of-sight mode. Then the value of $h$ is (Radius of the earth is 6400 km)

• A. 20 m
• B. 40 m
• C. 45 m
• D. 50 m

Answer 1

Answer: (C)

The maximum line-of-sight distance $d_M$ between two antennas having heights $h_T$ and $h_R$ is
$d_M=\sqrt{2R{h}_T}+\sqrt{2R{h}_R}$
where $R$ is the radius of the earth, $h_T$ and $h_R$ are the heights of the transmitting and receiving antennas respectively.
Here, $d_M=40km=40\times 10^{3}m,h_T=20m,h_R=h,R=6400km=6400\times 10^{3}m$
$\therefore 40\times 10^3=\sqrt{2\times 6400\times 10^3\times 20}+\sqrt{2\times 6400\times 10^3\times h}$
$40\times 10^3=16\times 10^3+\sqrt{2\times 6400\times 10^3\times h}$
$h=\frac{{\left[\left(40-16\right)\times 10^3\right]}^2}{2\times 64\times 10^5}=45m$