The height of the transmitting antenna, if TV | vedclass

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(D) The range $d$ of a transmitting antenna of height $h$ is given by the formula: $d = \sqrt{2 R_e h}$ where $R_e$ is the radius of the Earth. Given:

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$320$

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(D) The range $d$ of a transmitting antenna of height $h$ is given by the formula: $d = \sqrt{2 R_e h}$ where $R_e$ is the radius of the Earth. Given: $d = 64 \ km = 64 	imes 10^3 \ m$ $R_e = 6.4 	imes 10^6 \ m$ Squaring both sides, we get: $d^2 = 2 R_e h$ Rearranging for $h$: $h = \frac{d^2}{2 R_e}$ Substituting the values: $h = \frac{(64 	imes 10^3)^2}{2 	imes 6.4 	imes 10^6} = \frac{4096 	imes 10^6}{12.8 	imes 10^6} = \frac{4096}{12.8} = 320 \ m$

The height of the transmitting antenna, if $TV$ programs have to cover a population in an area of radius $64 \ km$, is: [Use Radius of earth $= 6.4 \times 10^6 \ m$] (in $m$)

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