A transmitting antenna has a height of 20 ,m. | vedclass

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Question

(D) The formula for the maximum line-of-sight $(LOS)$ distance $d_m$ between a transmitting antenna of height $h_T$ and a receiving antenna of height

Vedclass · Accepted Answer

$45$

Vedclass · Answer

(D) The formula for the maximum line-of-sight $(LOS)$ distance $d_m$ between a transmitting antenna of height $h_T$ and a receiving antenna of height $h_R$ is given by $d_m = \sqrt{2Rh_T} + \sqrt{2Rh_R}$, where $R$ is the radius of the Earth.Given: $h_T = 20 \,m$, $d_m = 40 \,km = 40,000 \,m$, and $R = 6400 \,km = 6.4 	imes 10^6 \,m$.Substituting the values:$40,000 = \sqrt{2 	imes 6.4 	imes 10^6 	imes 20} + \sqrt{2 	imes 6.4 	imes 10^6 	imes h_R}$$40,000 = \sqrt{256 	imes 10^6} + \sqrt{12.8 	imes 10^6 	imes h_R}$$40,000 = 16,000 + \sqrt{12.8 	imes 10^6 	imes h_R}$$24,000 = \sqrt{12.8 	imes 10^6 	imes h_R}$Squaring both sides:$(24,000)^2 = 12.8 	imes 10^6 	imes h_R$$576,000,000 = 12,800,000 	imes h_R$$h_R = \frac{576,000,000}{12,800,000} = 45 \,m$.Thus, the height of the receiving antenna is $45 \,m$.

$A$ transmitting antenna has a height of $20 \,m$. What will be the height of the receiving antenna if the maximum distance between them for satisfactory communication in line-of-sight $(LOS)$ mode is $40 \,km$ (in $\,m$)? (The radius of the Earth is $6400 \,km$.)

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