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A transmitting antenna at the top of a tower has a height of 36 m and the height of the receiving antenna is 49 m. What is maximum distance between them, for satisfactory communication is the LOS mode? (Radius of earth = 6400 km)

Text Solution

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Here `h_(T)=36m, h_(R)=49 and R=6400 km= 6400000 = 64 xx 10^(5)m`
`:.` Maximum line-of-sight (LOS) distance `d_(m)` between the two antennas is ltbr. `d_(M)=sqrt(2Rh_(T))+sqrt(2Rh_(R))`
`d_(M)=sqrt(2xx64xx10^(5)xx36)+sqrt(2xx64xx10^(5)xx49)`
`d_(M)=8xx6xx10^(2)xxsqrt(2xx10)+8xx7xx10^(2)xx sqrt(2xx10)=48xx10^(2)xxsqrt(20)+56xx10^(2)xxsqrt(20)`
`=104xx10^(2)xxsqrt(20)=104xx10^(2)xx2sqrt(5)=208xxsqrt(5)xx10^(2)=208xx2.23xx100=46384 m = 46.384 km`.
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