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Question
Solve the numerical problem.
Height of a TV tower is 600 m at a given place. Calculate its coverage range if the radius of the Earth is 6400 km. What should be the height to get the double coverage area?
Solution
Given: h = 600 m, R = 6.4 × 106 m
To find: Range (d)
Height to get the double coverage (h′)
Formula: d = `sqrt(2"hR")`
Calculation: From the formula,
d = `sqrt(2xx600xx6.4xx10^6)`
= 87.6 × 103
= 87.6 km
Now, for A′ = 2A
π(d′)2 = 2(πd2)
∴ (d′)2 = 2d2
From formula,
h′ = `(("d"^′)^2)/(2"R")`
= `(2"d"^2)/(2"R")`
= 2 × h ....`(∵ "h" = "d"^2/(2"R"))`
= 2 × 600
= 1200 m
The coverage range is 87.6 km and the height of antenna to double the area should be 1200 m.
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