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 $\mathbf{n} \%$.
The value of $n$, to the nearest integer, is .
Solution:
Range $=\sqrt{2 \mathrm{Rh}}$
Range (i) $=\sqrt{2 \mathrm{Rh}}$
Range (ii) $=\sqrt{2 \mathrm{Rh}}+\sqrt{2 \mathrm{Rh}^{\prime}}$
where $h=20 \mathrm{~m} \& \mathrm{~h}^{\prime}=5 \mathrm{~m}$
$A n s=\frac{\sqrt{2 R h^{\prime}}}{\sqrt{2 R h}} \times 100 \%=\frac{\sqrt{5}}{\sqrt{20}} \times 100 \%=50 \%$