A TV transmission tower of antenna is at a height of 20 m. How much service area can it cover if the receiving antenna is (i) at ground level (ii) at a height of 25 m ? Calculate the percentage increase in area covered in case (ii) relative to case (i).

Explanation

Here, `h_1 = 20 m, h_2 = 25m `
`(i) d = sqrt(2h_1R) = sqrt(2 xx 20 xx (6.4 xx 10^6)) = 16 xx 10^3 m = 16 km`
Area covered, `A = pid^2 = 22/7 xx (16)^2 = 804.6 km^2`
(ii) Range, `d_1 = sqrt(2h_1R) + sqrt(2h_2R) = sqrt(2 xx 20 xxx (6.4 xx 10^6)) + sqrt ( 2 xx 25 xx 6.4 xx 10^6)`
`= 16 km + 17.9 km = 33.9 km`
Area covered, `A_1 = pid_(1)^(2) = 22/7 xx (33.9)^2 = 3611.8 km^2`
`%` increase in area `= (A_1 - A)/A xx 100 = ((3611.8 - 804.6)/804.6) xx 100 = 348.9%`.