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
$d_{M}=\sqrt{2Rh_{T}}+\sqrt{2Rh_{R}}$
where $R$ is the radius of the earth, $h_T$ and $h_R$ are the heights of the transmitting and receiving antennas respectively.
Here, $d_{M} = 40\, km = 40 × 10^3\, m, h_{T} = 20\, m, h_{R} = h, R = 6400\, km = 6400 × 10^3\, m$
$\therefore 40\times10^{3}=\sqrt{2 × 6400 ×10^{3} × 20 }+\sqrt{2 × 6400 ×10^{3} × h}$
$40\times10^{3}=16\times10^{3} +\sqrt{2\times6400\times10^{3}\times h}$
$h=\frac{\left[\left(40-16\right)\times10^{3}\right]^{2}}{2\times64\times10^{5}}=45\,m$