Q 12-08-152JEE MainJEE Main 2021 (31 Aug, Shift 1)Medium
If the sum of the heights of transmitting and receiving antennas in the line of sight of communication is fixed at $160$ m, then the maximum range of LOS communication is ______ km. (Take radius of Earth $= 6400$ km)
Numerical value type. Enter your answer.
Answer: 64
Range $d = \sqrt{2Rh_T} + \sqrt{2Rh_R}$ with $h_T + h_R = 160$ m. This is maximum when $h_T = h_R = 80$ m.
$$d = 2\sqrt{2\times6.4\times10^6\times80} = 2\times3.2\times10^4\ \text{m} = 64\ \text{km}$$
Solution by Sreeraj P, M.Sc Physics