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  • The height of a transmitting antenna at the top of a tower is and that of receiving antenna is <i

The height of a transmitting antenna at the top of a tower is \mathrm{25m} and that of receiving antenna is \mathrm{49m}. The maximum distance between them, for satisfactory communication in \mathrm{LOS(Line-of-Sight)} is \mathrm{K\sqrt{5}\times10^{2}m}. The value of \mathrm{K} is __________.

( Assume radius of Earth is \mathrm{64\times10^{+5}m} ) [ Calculate upto nearest integer value ]

Option: 1

192


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

Here height of transmitting antenna  \mathrm{h_{T}=25m}

Height of receiving antenna  \mathrm{h_{R}=49m}

Maximum distance for LOS

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

    \mathrm{=\sqrt{2 R}\left(\sqrt{h_{R}}+\sqrt{h_{T}}\right)} \\

    \mathrm{=\sqrt{2 \times 64 \times 10^{5}} \times(\sqrt{49}+\sqrt{25}})\\

    \mathrm{=8 \times 10^{2} \times \sqrt{20} \times(7+5)} \\

    \mathrm{=96 \times 10^{2} \times 2 \sqrt{5}} \\

    \mathrm{=192 \sqrt{5} \times 10^{2}}

\mathrm{K=192 }

Hence the answer is \mathrm{192 }

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vinayak

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