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AP EAMCET · PHYSICS · Communication System

If the sum of heights of transmitting and receiving antennas in line of sight of communication is ' h ', then the height of receiving antenna, to have the range maximum is

  1. A \(\frac{h}{2}\)
  2. B \(\frac{\mathrm{h}}{4}\)
  3. C 2 h
  4. D \(\frac{2 \mathrm{~h}}{3}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{h}{2}\)

Step-by-step Solution

Detailed explanation

Given \(h_t + h_r = h \implies h_t = h - h_r\). Range \(D = \sqrt{2Rh_t} + \sqrt{2Rh_r} = \sqrt{2R(h - h_r)} + \sqrt{2Rh_r}\). For maximum range, \(\frac{dD}{dh_r} = 0\). \(\frac{d}{dh_r} \left( \sqrt{2R(h - h_r)} + \sqrt{2Rh_r} \right) = 0\).…
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