The maximum distance between the transmitting and receiving antenna for a satisfactory communication in LOS mode is 48 km. If the height of the receiving antenna is 80 m, then height of the transmitting antenna is: (Given radius of earth = 6400 km)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 80 m
The maximum communication distance (d) in the LOS mode is -
$d=\sqrt{2h_rR}+\sqrt{2h_tR}$
where,
$h_r$, Height of receiving antenna
$h_t$, Height of transmitted anteena
$48×10^3=\sqrt{2×80×6.4×10^6}+\sqrt{2×h_t×6.4×10^{-6}}$
$48×10^3=32×10^3+\sqrt{2×h_t×6.4×10^{-6}}$
$⇒h_t=\frac{(32×10^3)^2}{2×6.4×10^{-6}}$
$=\frac{32×32}{2×6.4}$
$≃80m$