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Need explanation for: - Communication Systems - JEE Main

In a line of sight radio communication a distance of about 50km is kept between the transmitting and receiving antennas. If the height of the receiving antennas 70 m, then the minimum height of the transmitting antenna should be: 

(Radius of the Earth= 6.4 \times 10^{6 }m)

  • Option 1)

    20 m

  • Option 2)

    51 m

  • Option 3)

    32 m

  • Option 4)

    40 m

 
Answers (1)
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R=6.4 \times 10^{6}

d=Range=50km

d=\sqrt{2Rh_{T}}+\sqrt{2Rh_{R}}

\Rightarrow 50 \times 10^{3}=\sqrt{2 \times 64 \times 10^{5} h_{T}}+\sqrt{2 \times 64 \times 10^{5} h_{R}}

\Rightarrow h_{T}=32m


Option 1)

20 m

Option 2)

51 m

Option 3)

32 m

Option 4)

40 m

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