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A transmitting antenna has a height $20 \mathrm{~m}$. What will be the height of receiving antenna, if the maximum distance between them for satisfactory communication in line-of-sight (LOS) mode is $40 \mathrm{~km}$ ? (The earth radius is $6400 \mathrm{~km}$.)
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Verified Answer
The correct answer is:
$45 \mathrm{~m}$
Given, height of transmitting antenna $h_t=20 \mathrm{~m}$, maximum line of sight (LOS) distance between receiving antenna and transmitting antenna $=40 \mathrm{~km}$ and radius of Earth, $R=6400 \mathrm{~km}$. The maximum line of sight distance,
$\begin{aligned}
& d_m=\sqrt{2 R h_T}+\sqrt{2 R h_R} \\
& \Rightarrow 40 \times 10^3=\sqrt{2 \times 6.4 \times 10^6 \times 20}+ \\
& \sqrt{2 \times 6.4 \times 10^6 \times x} \\
& \Rightarrow \sqrt{2 \times 6.4 \times 10^6 x}=24000 \\
& \Rightarrow x=45 \mathrm{~m}
\end{aligned}$
Hence, the correct option is (4).
$\begin{aligned}
& d_m=\sqrt{2 R h_T}+\sqrt{2 R h_R} \\
& \Rightarrow 40 \times 10^3=\sqrt{2 \times 6.4 \times 10^6 \times 20}+ \\
& \sqrt{2 \times 6.4 \times 10^6 \times x} \\
& \Rightarrow \sqrt{2 \times 6.4 \times 10^6 x}=24000 \\
& \Rightarrow x=45 \mathrm{~m}
\end{aligned}$
Hence, the correct option is (4).
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