Two identical antennas mounted on identical towers are separated from each other

Question:

Two identical antennas mounted on identical towers are separated from each other by a distance of $45 \mathrm{~km}$. What should nearly be the minimum height of receiving antenna to receive the signals in line of sight?

(Assume radius of earth is $6400 \mathrm{~km}$ )

  1. (1) $19.77 \mathrm{~m}$

  2. (2) $39.55 \mathrm{~m}$

  3. (3) $79.1 \mathrm{~m}$

  4. (4) $158.2 \mathrm{~m}$


Correct Option: 2,

Solution:

(2)

$\mathrm{D}=2 \sqrt{2 \mathrm{Rh}}$

$\mathrm{h}=\frac{\mathrm{D}^{2}}{8 \mathrm{R}}=\frac{45^{2}}{8 \times 6400} \mathrm{~km} \cong 39.55 \mathrm{~m}$

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