Multiple choice

A transmitting antenna at the top of a tower has a height 32 m and the height of the receiving antenna is 50 m. What is the maximum distance between them for satisfactory communication in LOS mode?. Given that radius of the earth is $6.4 \times 10^{6}m$

  1. 45.5 km

  2. 25.5 km

  3. 85.2 km

  4. 33.5 km
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A Correct answer
Explanation

The maximum distance d = sqrt(2*R*h1) + sqrt(2*R*h2). d = sqrt(2 * 6.4*10^6 * 32) + sqrt(2 * 6.4*10^6 * 50) = sqrt(409.6*10^6) + sqrt(640*10^6) = 20200 + 25300 = 45500 m = 45.5 km.

AI explanation

The maximum line of sight distance for communication is given by the formula d equals the square root of two times R times h sub one plus the square root of two times R times h sub two, where R is the radius of the earth and h sub one and h sub two are the antenna heights. Substituting the given values gives d equals the square root of two times 6400000 times 32 plus the square root of two times 6400000 times 50. This simplifies to the square root of 409600000 plus the square root of 640000000, which equals 20239 meters plus 25298 meters, yielding a total of 45537 meters. Converting this to kilometers gives a maximum satisfactory communication distance of 45.5 km.

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