The height of a transmission antenna is 100 , | vedclass

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Question

$(A)$ The range of the transmission antenna is given by $d = \sqrt{2hR_e}$.Here, $h = 100 \, m = 0.1 \, km$ and $R_e = 6400 \, km = 6.4 	imes 10^3 \,

Vedclass · Accepted Answer

$39.5 	imes 10^5$

Vedclass · Answer

$(A)$ The range of the transmission antenna is given by $d = \sqrt{2hR_e}$.Here, $h = 100 \, m = 0.1 \, km$ and $R_e = 6400 \, km = 6.4 	imes 10^3 \, km$.$d = \sqrt{2 	imes 0.1 	imes 6400} = \sqrt{1280} \approx 35.77 \, km$.The area covered is $A = \pi d^2 = \pi (2hR_e) = 2 \pi h R_e$.$A = 2 	imes 3.14 	imes 0.1 \, km 	imes 6400 \, km \approx 4021.2 \, km^2$.Population = $	ext{Area} 	imes 	ext{Population density} = 4021.2 \, km^2 	imes 1000 \, 	ext{people}/km^2 = 4,021,200 \approx 40 	imes 10^5$.Comparing with the given options, the closest value is $39.5 	imes 10^5$.

The height of a transmission antenna is $100 \, m$. The population density is $1000 \, \text{people}/km^2$. How many people can watch the program?

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