A TV transmission tower has a height of 240 m. Signals broadcast from this tower will be received by LOS communication at a distance of (assume the radius of the earth to be 6.4 × 106 m)
A TV transmission tower has a height of 240 m. Signals broadcast from this tower will be received by LOS communication at a distance of (assume the radius of the earth to be 6.4 × 106 m)

(a) 100 km

(b) 24 km

(c) 55 km
(d) 50 km

Answer:

The correct options are (b) 24 km (c) 55 km and (d) 50 km

Explanation:

{{h}_{T}}=240m

R=6.4\times {{10}^{6}}m

For, LOS communication we have:

{{d}_{T}}=\sqrt{2R{{h}_{T}}}

{{d}_{T}}=\sqrt{2\times 6.4\times {{10}^{6}}\times 240}=\sqrt{4\times 8\times {{10}^{6}}}

{{d}_{T}}=55.424km

So, the range 55.424 km covers the distances of 24 km, 55 km and 50 km.