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A transmission tower at a particular place has a height of 176m. (A) What is its coverage range? (B) By how much should the height be increased to 1.25 times its coverage range? Given that radius of earth = 6400 km.

1 Answer

Let $h$ be height of tower, $d$ be radius of coverage, and $R$ the radius of earth $\rightarrow$ $d=\sqrt{2Rh}$
Given $R = 6400 \;km$, and $h = 176\;m$, $d = \sqrt {2 \times 6400 \times 10^3 \times 176} = 47.46 \;km$
To calculate the new height to increase the coverage by 1.25 times, $\rightarrow \large\frac{d_1}{d_2}$$= \sqrt {\large\frac{h_1}{h2}}$
Given $d_2 = 1.25\times d_1$ and $h_1 = 176\;m$, we can calculate $h_2 = 176\times \large\frac{1.25^2}{1^1}$$ = 176 \times 1.25 \times 1.25 = 275\;m$
answered Jul 13, 2014 by balaji.thirumalai

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