Question

A TV transmitting antenna is $75$m tall. How much maximum distance and area cover by it? Radius of Earth $=6.4\times {10}^6$m

Answer 1

Height of antenna h = 75 m

Radius of the Earth R $=6.4\times {10}^6$ m

(i) $\therefore$ Maximum distance of transmitting

$d=\sqrt{2Rh}$

$d=\sqrt{2\times 6.4\times {10}^6\times 75}$

$=\sqrt{960\times {10}^6}m=30.98\times {10}^{3}m$

$d=31km$

(ii) Maximum area covered by transmitting

A $=\pi d^2$

A $=\pi \left(2Rh\right)$

A $=3.14\times 960\times {10}^6{m}^2=3014\times {10}^6{m}^2$

A $=3014k{m}^2$