Question

If the heights of transmitting and the receiving antennas are each equal to h, the maximum line-of-sight distance between them is (R is the radius of the earth)

• A. $\sqrt{2Rh}$
• B. $\sqrt{4Rh}$
• C. $\sqrt{6Rh}$
• D. $\sqrt{8Rh}$
• E. $\sqrt{Rh}$

Answer 1

Answer: (D)

$\sqrt{8Rh}$

We know that,
Maximum line of sight distance
$d_m=d_r+d_R=\sqrt{2R{h}_T}+\sqrt{2R{h}_R}$ $(\because h_T=h_R=h)$
$\therefore d_m=\sqrt{2Rh}+\sqrt{2Rh}$
$d_m=2\sqrt{2Rh}=\sqrt{4\times 2Rh}=\sqrt{8Rh}$