A T.V. transmission tower at a particular station has a height of `160 m` .
(a) What is its coverage range ?
(b) How much population is covered by transmission , if the average population density around the tower is `1200 km^(-2)`?
( c ) By how much the height of tower be increased to double its coverage range ?
Given radius of earth ` = 6400 km`.

Answer

` (a) 45255 m ,(b) 77.24 lakh , ( c ) 480 m`

Explanation

(a) Coverage range ,
` d = sqrt( 2 hR) = sqrt( 2 xx 160 xx 6.4 xx 10^(6))`
` = 45255 m = 45.255 km`
(b) Population covered ` = rho xx pi d^(2)`
`= 1200 xx (22)/( 7) xx ( 45.255)^(2)`
`= 77.24 xx 10^(5) = 77.24 lakh`
( c ) `d' = sqrt( 2h' R) = 2d = 2 sqrt( 2 h R)`
`h' = 4 h = 4 xx 160 = 640 m`
Increase in height of tower ` = h' - h`
`= 640 - 160 = 480 m`