The heights of transmitting and receiving ant | vedclass

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Question

(B) The maximum distance $d_m$ between the transmitting antenna of height $h_t$ and the receiving antenna of height $h_r$ for line-of-sight communicat

Vedclass · Accepted Answer

$96$

Vedclass · Answer

(B) The maximum distance $d_m$ between the transmitting antenna of height $h_t$ and the receiving antenna of height $h_r$ for line-of-sight communication is given by the formula: $d_m = \sqrt{2Rh_t} + \sqrt{2Rh_r}$.Given: $R = 6.4 	imes 10^6 \ m$,$h_t = \frac{R}{20000}$,and $h_r = \frac{R}{80000}$.Substituting the values:$d_m = \sqrt{2R \cdot \frac{R}{20000}} + \sqrt{2R \cdot \frac{R}{80000}}$$d_m = R \sqrt{\frac{2}{20000}} + R \sqrt{\frac{2}{80000}}$$d_m = R \sqrt{\frac{1}{10000}} + R \sqrt{\frac{1}{40000}}$$d_m = R \cdot \frac{1}{100} + R \cdot \frac{1}{200}$$d_m = R \left( \frac{2+1}{200} ight) = R \cdot \frac{3}{200}$$d_m = (6.4 	imes 10^6) \cdot \frac{3}{200} = 6.4 	imes 10^4 \cdot 1.5 = 9.6 	imes 10^4 \ m = 96 \ km$.

The heights of transmitting and receiving antennas are respectively $\frac{1}{20000}$ and $\frac{1}{80000}$ times the radius of the earth. The maximum distance between these two antennas for satisfactory communication in line of sight mode is (Radius of the earth $= 6.4 \times 10^6 \ m$) (in $km$)

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