A transmitting antenna is kept on the surface of the earth. The minimum height of receiving antenna required to receive the signal in line of sight at 4 km distance from it is $$x \times 10^{-2}$$ m. The value of $$x$$ is _____.
(Let, radius of earth R = 6400 km)

For line of sight communication, the maximum distance $$d$$ at which a signal can be received is related to the antenna height $$h$$ by:

$$d = \sqrt{2Rh}$$

where $$R$$ is the radius of the Earth.

Since the transmitting antenna is on the surface (height = 0), we need the receiving antenna at height $$h$$ such that:

$$d = \sqrt{2Rh}$$

$$d^2 = 2Rh$$

$$h = \frac{d^2}{2R}$$

We are given that $$d = 4$$ km = $$4000$$ m, $$R = 6400$$ km = $$6.4 \times 10^6$$ m

$$h = \frac{(4000)^2}{2 \times 6.4 \times 10^6} = \frac{16 \times 10^6}{12.8 \times 10^6} = 1.25 \text{ m}$$

$$h = 125 \times 10^{-2} \text{ m}$$

Therefore, $$x = 125$$.