Question

A T.V transmitting Antenna is $128m$ tall. If the receiving Antenna is at the ground level, the maximum distance between them for satisfactory communication in L.O.S. mode is:

[Radius of the earth $=6.4\times {10}^{6}m$]

• A. $64\times \sqrt{10}km$
• B. $\frac{128}{\sqrt{10}}km$
• C. $128\times \sqrt{10}km$
• D. $\frac{64}{\sqrt{10}}km$

Answer 1

Answer: (B)

$\frac{128}{\sqrt{10}}km$

Height of transmitting antenna, $h_T=128m$

Radius of earth, $R=6.4\times {10}^{6}m$

Receiving antenna is at ground level, i.e., $h_R=0$

$\therefore$ The distance between the antennas: $d=\sqrt{2h_{T}R}$

$\therefore d=\sqrt{2\times 128\times 6.4\times {10}^6}=\frac{128}{\sqrt{10}}\times {10}^{3}m$

$⟹$ $d=\frac{128}{\sqrt{10}}km$