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

$d = \sqrt {2h_tR_e}+\sqrt {2 \times h_RR_e}$
$= \sqrt {2 \times 25 \times 64 \times 10^5}+ \sqrt {2 \times 49 \times 64 \times 10^5}$
$= 8000\sqrt 5 +11200\sqrt 5\ m$
$= 19200\sqrt 5\ m$
$= 192\sqrt 5 \times 10^2\ m$
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 $192$.