The height of a transmission antenna is 49 ,m | vedclass

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(B) The maximum line-of-sight distance $d_{\max}$ between a transmitting antenna of height $h_T$ and a receiving antenna of height $h_R$ is given by t

Vedclass · Accepted Answer

$53.6$

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(B) The maximum line-of-sight distance $d_{\max}$ between a transmitting antenna of height $h_T$ and a receiving antenna of height $h_R$ is given by the formula: $d_{\max} = \sqrt{2Rh_T} + \sqrt{2Rh_R}$ where $R$ is the radius of the Earth,approximately $6400 \,km = 6.4 	imes 10^6 \,m$. Given: $h_T = 49 \,m$,$h_R = 64 \,m$,$R = 6.4 	imes 10^6 \,m$. Substituting the values: $d_{\max} = \sqrt{2 	imes 6.4 	imes 10^6 	imes 49} + \sqrt{2 	imes 6.4 	imes 10^6 	imes 64}$ $d_{\max} = \sqrt{12.8 	imes 10^6 	imes 49} + \sqrt{12.8 	imes 10^6 	imes 64}$ $d_{\max} = 10^3 	imes \sqrt{12.8} 	imes (7 + 8)$ $d_{\max} = 10^3 	imes 3.577 	imes 15$ $d_{\max} \approx 53660 \,m = 53.66 \,km$. Thus,the maximum distance is approximately $53.6 \,km$.

The height of a transmission antenna is $49 \,m$ and that of the receiving antenna is $64 \,m$. What should be the maximum distance between them for line of sight transmission (in $\,km$)?

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