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JEE Main 202131 AugustMorning Shift
Exam
JEE Main
Year
2021
Date
31 August
Shift
Morning Shift
Subject
Physics
Chapter
Communication System

JEE Main 2021 · 31 August · Morning Shift · Physics · Communication System

If the sum of the heights of transmitting and receiving antennas in...

If the sum of the heights of transmitting and receiving antennas in the line of sight of communication is fixed at 160m,160m, then the maximum range of LOS communication is _______ kmkm (Take radius of Earth =6400km= 6400km)

Correct answer

0

Step-by-step solution

hr+ht=160{h}_{r} + {h}_{t} = 160 (Given)
LOS=2R(hr+ht)LOS = \sqrt{2R}\left(\sqrt{{h}_{r}} + \sqrt{{h}_{t}}\right)
LOS=2R(hr+160−hr)LOS = \sqrt{2R}\left(\sqrt{{h}_{r}} + \sqrt{160 - {h}_{r}}\right)
dLOSdhr=0=2R(12hr−12160−hr)=0\dfrac{dLOS}{d{h}_{r}} = 0 = \sqrt{2R}\left(\dfrac{1}{2\sqrt{{h}_{r}}} - \dfrac{1}{2\sqrt{160 - {h}_{r}}}\right) = 0
hr=ht=80m{h}_{r} = {h}_{t} = 80m
LOS=2R(80+80)=22×6400×103×80=64kmLOS = \sqrt{2R} ( \sqrt{80} + \sqrt{80} ) = 2\sqrt{2 \times 6400 \times {10}^{3} \times 80} = 64km
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