A transmitting antenna of height $ h $ and the receiving antenna of height $ 45 \mathrm{~m} $ are separated by a distance of $ 40 \mathrm{~km} $ of satisfactory communication in line-of-sight mode. Then, the value of $ h $ is (given, radius of earth is $ 6400 \mathrm{~km} $ ),

Question

A transmitting antenna of height $ h $ and the receiving antenna of height $ 45 \mathrm{~m} $ are separated by a distance of $ 40 \mathrm{~km} $ of satisfactory communication in line-of-sight mode. Then, the value of $ h $ is (given, radius of earth is $ 6400 \mathrm{~km} $ ),, $ 15 \mathrm{~m} $, $ 20 \mathrm{~m} $, $ 30 \mathrm{~m} $, $ 25 \mathrm{~m} $

MARKS App · Accepted Answer

Given: Height of transmitting antenna, h t = h , height of receiving antenna, h r = 45 m , distance between the two antennas, D = 40 km , radius of earth, R = 6400 km . For line-of-sight mode communication, above terms are related as, D = 1 2 R h t + 1 2 R h r ⇒ 1 2 R h t = D - 1 2 R h r ⇒ 1 2 R h t = D - 1 2 R h r 2 ⇒ h t = 1 2 R D - 1 2 R h r 2 ⇒ h t = 1 2 × 6 . 4 × 10 6 × 4 × 10 4 - 1 2 × 6 . 4 × 10 6 × 45 2 = 20 m

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