A TV transmitting antenna is 128 m tall. If | vedclass

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Question

(B) The maximum line-of-sight distance $d$ for a transmitting antenna of height $h_T$ and a receiving antenna at ground level is given by the formula:

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$\frac{128}{\sqrt{10}} \ km$

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(B) The maximum line-of-sight distance $d$ for a transmitting antenna of height $h_T$ and a receiving antenna at ground level is given by the formula: $d = \sqrt{2 R_e h_T}$.Given:$R_e = 6.4 	imes 10^6 \ m$$h_T = 128 \ m$Substituting the values:$d = \sqrt{2 	imes (6.4 	imes 10^6) 	imes 128}$$d = \sqrt{12.8 	imes 10^6 	imes 128}$$d = \sqrt{128 	imes 10^5 	imes 128}$$d = 128 	imes \sqrt{10^5} \ m$$d = 128 	imes \sqrt{10 	imes 10^4} \ m$$d = 128 	imes 100 \sqrt{10} \ m$$d = 12800 \sqrt{10} \ m$Converting to kilometers $(1 \ km = 1000 \ m)$:$d = \frac{12800 \sqrt{10}}{1000} \ km = 12.8 \sqrt{10} \ km$Wait,checking the calculation again:$d = \sqrt{2 	imes 6.4 	imes 10^6 	imes 128} = \sqrt{12.8 	imes 10^6 	imes 128} = \sqrt{1638.4 	imes 10^6} = \sqrt{16.384 	imes 10^8} = 40477 \ m \approx 40.5 \ km$.Re-evaluating the provided options: $128/\sqrt{10} \approx 128/3.16 \approx 40.5 \ km$. Thus,option $B$ is correct.

$A$ $TV$ transmitting antenna is $128 \ m$ tall. If the receiving antenna is at the ground level,the maximum distance between them for satisfactory communication in line-of-sight mode is (radius of the earth $R_e = 6.4 \times 10^6 \ m$):

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