If a line of sight radio communication, a distance of about $$50$$ km is kept between the transmitting and receiving antennas. If the height of the receiving antenna is $$70$$ m, then the minimum height of the transmitting antenna should be (Radius$$ of the earth $$=$$ $$6.4$$×$$106$$ $$m)

Question

If a line of sight radio communication, a distance of about $$50$$ km is kept between the transmitting and receiving antennas. If the height of the receiving antenna is $$70$$ m, then the minimum height of the transmitting antenna should be (Radius$$ of the earth $$=$$ $$6.4$$×$$106$$ $$m)

Infinity Learn · Accepted Answer

In the line of sight communication, distance d between transmitting antenna and receiving antenna is given by $$d=2RhT+2RhR$$ Here in figure,  hR and  hT  is the height of receiving and transmitting antenna, respectively.  ∴$$d=2RhT+2RhR$$ ⇒$$50$$×$$103$$ $$=$$ $$2RhT+hR$$ ⇒$$50$$×$$103$$ $$=2(6.4$$×$$106)hT+70$$ ⇒$$hT=50$$×$$1033577.7$$−$$8.37$$ $$=13.98-8.37=5.61$$ ⇒hT $$=$$ $$31.5$$ ≃ $$32$$ m

If a line of sight radio communication, a distance of about 50 km is kept between the transmitting and receiving antennas. If the height of the receiving antenna is 70 m, then the minimum height of the transmitting antenna should be (Radius of the earth = $6.4 \times 10^{6}$ m)

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If a line of sight radio communication, a distance of about 50 km is kept between the transmitting and receiving antennas. If the height of the receiving antenna is 70 m, then the minimum height of the transmitting antenna should be (Radius of the earth = 6.4×106 m)

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Ready to Test Your Skills?

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If a line of sight radio communication, a distance of about 50 km is kept between the transmitting and receiving antennas. If the height of the receiving antenna is 70 m, then the minimum height of the transmitting antenna should be (Radius of the earth = $6.4 \times 10^{6}$ m)