Q 12-08-173JEE MainJEE Main 2021 (27 Aug, Shift 1)Easy
A transmitting antenna has a height of $320$ m and that of receiving antenna is $2000$ m. The maximum distance between them for satisfactory communication in line of sight mode is $d$. The value of $d$ is ______ km.
Numerical value type. Enter your answer.
Answer: 224
Taking the radius of the earth as $6400$ km:
$$d = \sqrt{2Rh_T} + \sqrt{2Rh_R} = \sqrt{2\times6.4\times10^6\times320} + \sqrt{2\times6.4\times10^6\times2000}$$
$$d = 64\ \text{km} + 160\ \text{km} = 224\ \text{km}$$
Solution by Sreeraj P, M.Sc Physics