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Question

The T.V transmission tower in Delhi has a height of 240 m. The distance up to which the broadcast can be received (taking the radius of earth to be 6.4×106m) is (in km) (round off to nearest integer)

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Solution

Let h be the height of the tower, Re be the radius of the earth. The waves can be received at a maximum distance of l from the tower, due to the curvature of the earth's surface.



From the right angled triangle in figure,
l2+R2e=(Re+h)2
l2=2Reh+h2
l2=2Reh
[since h<<Re]

x=2×2401000×6400 km
x=8×43 km32×1.755 km

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