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# Question and Answer

## QuestionPhysicsClass 12

A transmitting antenna at the top of a tower has a height $$32\;m$$ and the height of the receiving antenna is $$50\;m$$. What is the maximum distance between them for satisfactory communication in $$LOS$$ mode? Given radius of earth $$6.4\times 10^6\;m$$.

$$45.5\ \mathit{km}$$
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## Solution

Given:
Radius of Earth, $$R=6.4\times 10^6\;m$$
Height of transmitting antenna,$$h_t=32\;m$$
Height of receiving antenna, $$h_r=50\;m$$
Maximum distance for satisfactory communication $$(d_m)$$  is given by,
$$d_m=\sqrt{2h_tR}+\sqrt{2h_rR}$$
$$d_m=\sqrt{2\times 32\times6.4\times 10^6}+\sqrt{2\times 50\times 6.4\times 10^6}$$
$$d_m=20,238.57+25,298.22$$
$$d_m=45,536.79 \ m$$
$$d_m=45.5\ \mathit{km}$$
Hence, maximum distance between them for satisfactory communication in LOS mode is $$45.5\ \mathit{km}$$.