A TV transmitter has a range of $50 \mathrm{~km}$. The height of the TV transmitter is _________ (Radius of…

A TV transmitter has a range of $50 \mathrm{~km}$. The height of the TV transmitter is _________ (Radius of the earth, $R_e=6 \cdot 4 \times \overline{10^6 \mathrm{~m} \text {) }}$
  1. 195.3 m
  2. 186.5 m
  3. 206 m
  4. 175 m

Solution

Range, $d=\sqrt{2 R_e h_T}$
$\begin{gathered}
50 \mathrm{~km}=\sqrt{2 \times 6.4 \times 10^6 \times h_T} \\
2500 \times 10^6=128 \times 10^5 h_T \\
\frac{25000}{128}=h_T \\
h_T=195.3
\end{gathered}$

Asked in: AP EAMCET 2018 (23 Apr Shift 1)

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