The maximum distance between the transmitting and receiving antennas for satisfactory communication in line…

The maximum distance between the transmitting and receiving antennas for satisfactory communication in line of sight mode is 57.6 km . If the height of the receiving antenna is 80 m , the height of the transmitting antenna is (Radius of earth $=6.4 \times 10^6 \mathrm{~m}$ )
  1. 28.8 m
  2. 51.2 m
  3. 25.6 m
  4. 14.4 m

Solution

$\begin{aligned} & \text { Range }=57.6 \mathrm{~km}, \mathrm{~h}_{\mathrm{r}}=80 \mathrm{~m}, \mathrm{R}=6.4 \times 10^6 \mathrm{~m} \\ & \therefore \text { Range }=\sqrt{2 \mathrm{Rh}_{\mathrm{r}}}+\sqrt{2 \mathrm{Rh}_{\mathrm{t}}} \\ & \Rightarrow 57.6 \times 10^3=\sqrt{2 \times 6.4 \times 10^6 \times 80}+\sqrt{2 \times 6.4 \times 10^6 \times \mathrm{h}_{\mathrm{t}}} \\ & \therefore \mathrm{h}_{\mathrm{t}}=51.2 \mathrm{~m}\end{aligned}$

Asked in: AP EAMCET 2024 (22 May Shift 1)

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