A transmitting antenna of height 25 m is fitted at the top of a tower of height 20m. What is the height of the receiving antenna from ground level if the maximum distance between transmitting antenna and receiving antenna on ground is 56 km. Radius of earth = 6400 km.

Explanation

Here, height of transmitting antenna
`h_(T) = 25+ 20 = 45m`,
Maximum distance between transmitting and
receiving antenna.
`d = 56km = 56 xx 10^3 m`.
Let `h_(R)` be the height of receiving antenna in metre.
As, `d = sqrt(2Rh_(T)) + sqrt(2Rh_(R))`
`:. 56 xx 10^3`
` = sqrt(2xx(6400 xx 10^3) xx 45) + sqrt(2 xx(6400 xx 10^3) xx h_(R))`
or ` 56 xx 10^3 = 24 xx 10^3 + sqrt (2 xx 6400 xx 10^3 xx h_R)`
or ` 2 xx 64 xx 10^5 xx h_R = [(56 - 24) xx 10^3]^2`
`(32 xx 10^3)^2`
`h_(R) = (32 xx 10^3)^2/(2xx64 xx 10^5) = 80m` .