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25/01/2022 1:34 pm
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If the sum of the heights of transmitting and receiving antennas in the line of sight of communication is fixed at 160 m, then the maximum range of LOS communication is _____km.
(Take radius of Earth = 6400 km)
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25/01/2022 1:45 pm
hT = hR = 160 ......(i)
d = \(\sqrt{2Rh_T} + \sqrt{2Rh_R}\)
d = \(\sqrt{2R} \Big[ \sqrt{h_T} + \sqrt{h_R}\Big]\)
d = \(\sqrt{2R} \Big[ \sqrt{x} + \sqrt{160 - x}\Big]\)
\(\frac{d(d)}{dx}\) = 0
\(\frac{1}{2 \sqrt x}\) + \(\frac{1 (-1)}{2 \sqrt{160 - x}}\) = 0
\(\frac{1}{\sqrt x}\) = \(\frac{1}{\sqrt{160 - x}}\)
x = 80 m
dmax = \(\sqrt{2 \times 6400}\)\(\Big[\sqrt{\frac{80}{1000}} + \sqrt{\frac{20}{1000}}\Big]\)
= \(\frac{80 \sqrt 2 \times 2 \sqrt{80}}{10 \sqrt{10}}\)
= 8 x 2 x √2 x 2√2 = 64 km