Q. A transmitting antenna of height $h$ and the receiving antenna of height $45\ m$ are separated by a distance of $40\ km$ for satisfactory communication in line of sight mode. Then the value of $h$ is
A) 15 $m$
B) 20$m$
C) 30 $m$
D) 25 $m$
Explanation
(b) $d = \sqrt{2Rh_{T}} + \sqrt{2Rh_{R}}$
$\therefore 40 \times 1000 = \sqrt{2 \times 6.4 \times 10^{6} \times h} + \sqrt{2 \times 6.4 \times 10^{6} \times 45}$
$40 \times 10^{3} = \sqrt{2 \times 6.4 \times 10^{6} \times h} + 24 \times 10^{3}$
$h = \frac{\left\lbrack (40 - 24)10^{3} \right\rbrack^{2}}{2 \times 6.4 \times 10^{6}} = 20\ m$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.