Question

The T.V transmission tower in Delhi has a height of $240\text{m}$. The distance up to which the broadcast can be received (taking the radius of earth to be $6.4\times {10}^{6}m)$ is (in km) (round off to nearest integer)

Answer 1

Let $h$ be the height of the tower, $R_e$ be the radius of the earth. The waves can be received at a maximum distance of l from the tower, due to the curvature of the earth's surface.



From the right angled triangle in figure,
$l^2+R_e^2=(R_e+h{)}^2$
$\Rightarrow l^2=2R_{e}h+h^2$
$\Rightarrow l^2=2R_{e}h$
[since $h<<R_e$]

$\Rightarrow x=\sqrt{2\times \frac{240}{1000}\times 6400\text{km}}$
$\Rightarrow x=8\times 4\sqrt{3}\text{km}\approx 32\times 1.7\approx 55\text{km}$