Question

A transmitting antenna at the top tower has a height 18 m and the height of the receiving antenna is 32 m. The maximum distance between them for satisfactory communication in line of sight mode is (Radius of earth = 6.4 x 106 m)

• A. 15.15 km
• B. 21.25 km
• C. 30.45 km
• D. 35.42 km

Answer 1

Answer: (D)

35.42 km

Answer 2

: Here $h_{T} = 10m,h_{R} = 32m$

$R = 6.4 \times 10^{6}m = 64 \times 10^{5}m$

The maximum line of single distance

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

$= \sqrt{2 \times 64 \times 10^{5} \times 18} + \sqrt{2 \times 64 \times 10^{5} \times 32}$

$= 48 \times 10^{2}\sqrt{10} + 64 \times 10^{2}\sqrt{10}$

$= 112 \times 10^{2} \times \sqrt{10}m$

$= 35417.5m = 35.42km$