A TV transmission tower antenna is at a height

Question:

A TV transmission tower antenna is at a height of $20 \mathrm{~m}$. Suppose that the receiving antenna is at.

(i) ground level

(ii) a height of $5 \mathrm{~m}$.

The increase in antenna range in case (ii) relative to case (i) is $\mathrm{n} \%$

The value of $\mathrm{n}$, to the nearest integer, is.

Solution:

(50)

Range $=\sqrt{2 \mathrm{Rh}}$

Range (i) $=\sqrt{2 \mathrm{Rh}}$

Range (ii) $=\sqrt{2 \mathrm{Rh}}+\sqrt{2 \mathrm{Rh}^{\prime}}$

where $\mathrm{h}=20 \mathrm{~m} \& \mathrm{~h}^{\prime}=5 \mathrm{~m}$

Ans $=\frac{\sqrt{2 \mathrm{Rh}^{\prime}}}{\sqrt{2 \mathrm{Rh}}} \times 100 \%=\frac{\sqrt{5}}{\sqrt{20}} \times 100 \%=50 \%$

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