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A transmitting antenna at the top of a t...

A transmitting antenna at the top of a tower has a height of 50 m and the height of the receiving antenna is 32 m. What is the maximum distance between them for satisfactory communication in line of sight mode ?
(Radius of the earth (R ) =`6.4xx10^6` m) (`sqrt10`=3.16)

A

75.5 km

B

65 .5 km

C

55 .5 km

D

45 .5 km

Text Solution

Verified by Experts

The correct Answer is:
D
The maximum distance of the line of sight is `d_M=sqrt(2Rh_T) + sqrt(2 Rh_R)` where R is the radius of the earth
`sqrt(2xx64xx10^5xx50)+sqrt(2xx64xx10^5xx32)`
`=80xx10^2sqrt10+64xx10^2sqrt10
`=(80+64) xx 10^2 sqrt10`
`=144xx10^2 sqrt10`
`=455xx10^2 =45.5xx10^3` m =45.5 Km
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