A transmitting antenna has a height 20 m. What will be the height of receiving antenna, if the maximum distance between them for satisfactory communication in line-of-sight (LOS) mode is 40 km ? ( The earth radius is 6400 km. )

Options

A. 25 m
B. 30 m
C. 60 m
D. 45 m

Answer

D

Explanation

Given, height of transmitting antenna
`h_(t)=20m`, maximum line of sight (LOS) distance between receiving antenna and transmitting
antenna `=40km` and radius of Earth,
`R=6400 km`. The maximum line of sight distance,
`d_(m)=sqrt(2RP_(T))+sqrt(2Rh_(R))`
`rArr 40xx10^(3)=sqrt(2xx6.4xx10^(6)xx20)+sqrt(2xx6.4xx10^(6)xx x)`
`rArr sqrt(2xx6.4 xx10^(6)x)=24000`
`rArr x=45m`
Hence, the correct option is (d).