The transmitting antenna placed at the top of a tower has a height of 45 m from the ground. The distance between receiving and transmitting antennas is 40 km and the radius of earth is 6400 km .
The minimum height (in m) at which the receiving antenna is to be placed for satisfactory communication in LOS made, is

Options

A. 5
B. 15
C. 20
D. 25

Answer

C

Explanation

Key Idea The maximum line of right distance `d_m` between two transmitting antenna of height `h_T` and receiving antenna of height `h_R` above the earth is given by
`d_m = sqrt(2Rh_T)+sqrt(2Rh_R)`
as, given that height of transmitting antenna, `h_T = 45xx10^(-3) `km distance between receiving and transmitting antenna `d_m = 40 km` and radius of earth R= 6400 km
Let height of receiving antenna `h_R=x`
By putting the values in above expression
`40= sqrt(2xx6400xx45xx10^(-3))+sqrt(2xx6400xx"x"xx10^(-3))`
`40= 24 + sqrt(2xx6.4 xx x)`
`x=((40-24)^2)/(2xx6.4) = 20 m`