A transmitting antenna of height 20 m and the receiving antenna of height h are separated by a distance of 40 km for satisfactory communication in line of sight (Los) mode. Then the value of his
(Give, radius of earth is 6400 km.

Options

A. 40 m
B. 45 m
C. 30 m
D. 25 m

Answer

B

Explanation

Given, height of transmitting antenna
`h_(T) = 20 `m, distance of LOS, `d_(m) = 40` km
As maximum distance of line of sight mode
`d_(m) = sqrt(2Rh_(T)) + sqrt(2Rh_(R))`
putting the given values, we get
`40 = sqrt( 2xx 6.4 xx 10^(3) xx 20 xx 10^(-3))`
`+sqrt(2xx 6.4xx 10^(3) xxh_(R) xx 10^(-3))`
`40 = 16 + sqrt( 2xx 6.4 xx 10^(3) xx 10^(-3) xxh_(R)) `
`rArr 2 xx 6.4 xx h_(T) = 24 xx 24`
`rArr h_(T) = 45 m`
Hence, the correct option is (b).