Question

A TV transmission tower has a height of $140m$ and the height of the receiving antenna is $40m$. What is the maximum distance up to which signals can be broadcasted from this tower in LOS(Line of Sight) mode? (Given: radius of the earth $=6.4\times {10}^{6}m$)

• A. $40km$
• B. $80km$
• C. $65km$
• D. $48km$

Answer 1

The correct option is C

$65km$

Step 1. Given Data:

Height of the TV tower $h_T=140m$

Height of the receiving antenna $h_R=40m$

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

Step 2. Calculate the Range:

If $d$is the range of the tower then,

$d=\sqrt{2h_{T}R}+\sqrt{2h_{R}R}$

$=\sqrt{2\times 140\times 6.4\times {10}^6}+\sqrt{2\times 40\times 6.4\times {10}^6}$

$=65km$

Hence option (C) is correct.