What should be the height of the transmitting | vedclass

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(A) The radius covered by the antenna is given by $r = \sqrt{2 R_e H_T}$.Given $r = 150 \, km = 1.5 	imes 10^5 \, m$ and $R_e = 6.5 	imes 10^6 \, m$

Vedclass · Accepted Answer

Height $= 1731 \, m$,Population Covered $= 1413 	imes 10^5$

Vedclass · Answer

(A) The radius covered by the antenna is given by $r = \sqrt{2 R_e H_T}$.Given $r = 150 \, km = 1.5 	imes 10^5 \, m$ and $R_e = 6.5 	imes 10^6 \, m$.Squaring both sides: $r^2 = 2 R_e H_T$.$H_T = \frac{r^2}{2 R_e} = \frac{(1.5 	imes 10^5)^2}{2 	imes 6.5 	imes 10^6} = \frac{2.25 	imes 10^{10}}{13 	imes 10^6} \approx 1730.76 \, m \approx 1731 \, m$.The population covered is the area covered multiplied by the population density.Area $= \pi r^2 = 3.14 	imes (150 \, km)^2 = 3.14 	imes 22500 \, km^2 = 70650 \, km^2$.Population $= 	ext{Area} 	imes 	ext{Density} = 70650 \, km^2 	imes 2000 \, / km^2 = 141300000 = 1413 	imes 10^5$.

What should be the height of the transmitting antenna and the population covered if the television telecast is to cover a radius of $150 \, km$? The average population density around the tower is $2000 \, / km^2$ and the value of $R_e = 6.5 \times 10^6 \, m$.

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