Question

The height of a transmitting antenna at the top of a tower is 25 m and that of receiving antenna is, 49 m. The maximum distance between them, for satisfactory communication in LOS (Line-Of-Sight) is \(K\sqrt5\times10^2\ m\). The value of K is ______ .
(Assume radius of Earth is \(64×10^5\ m\))
[Calculate upto nearest integer value]

Answer 1

Correct Answer: 192

\(d = \sqrt {2h_tR_e}+\sqrt {2 \times h_RR_e}\)
\(= \sqrt {2 \times 25 \times 64 \times 10^5}+ \sqrt {2 \times 49 \times 64 \times 10^5}\)
\(= 8000\sqrt 5 +11200\sqrt 5\ m\)
\(= 19200\sqrt 5\ m\)
\(= 192\sqrt 5 \times 10^2\ m\)
The maximum distance between them, for satisfactory communication in LOS (Line-Of-Sight) is \(k\sqrt 5×10^2\ m\).
Then, \(k = 192\)

So, the answer is \(192\).