Question

A transmitting antenna of height 20 m and the receiving antenna of height h are separated by a distance of 40 km for satisfactory communication in line of sight mode. Then the value of h is

(Given radius of the earth is 6400 km)

• A. 40 m
• B. 45 m
• C. 30 m
• D. 25 m

Answer 1

Answer: (B)

45 m

Answer 2

: $d_{M} = \sqrt{2Rh_{R}} + \sqrt{2Rh_{T}}$

Where $h_{R}$and$h_{T}$are the heights of receiving and transmitting antenna and R is the radius of the earth

$40 \times 10^{3} = \sqrt{2 \times 6400 \times 10^{3} \times h} + \sqrt{2 \times 6400 \times 10^{3} \times 20}$

$40 \times 10^{3} = \sqrt{2 \times 6400 \times 10^{3} \times h} + 16 \times 10^{3}$

$h = \frac{\lbrack(40 - 16) \times 10^{3}\rbrack^{2}}{2 \times 6.4 \times 10^{6}} = 45m$