In order to cover a circular region of radius 16 km, by a TV transmitter What must be the height of the transmitting antenna? (Radius of the earth = 6400 km),choose the correct option from the given options.
(A) 0.02 km
(B) 0.2 km
(C) 0.1 km
(D) 2 km
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Answer:
(A) 0.02 km
Explanation:
Radius of the circular region = 16 km (Given)
Radius of the earth = 6400 km (Given)
Let the range = d = 16 km and the height = h
Thus, according to the equation -
d = √2hr
= h = d²/2R
= h = 16 × 16 / 2 × 6400
= h = 256 / 12800
= h = 64/3200
= h = 0.02
Therefore, the height of the transmitting antenna should be 0.02 km.
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