Solveeit Logo

Question

Question: A transmitting antenna at the top tower has a height 18 m and the height of the receiving antenna is...

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

35.42 km

Explanation

Solution

: Here hT=10m,hR=32mh_{T} = 10m,h_{R} = 32m

R=6.4×106m=64×105mR = 6.4 \times 10^{6}m = 64 \times 10^{5}m

The maximum line of single distance

dm=2RhT+2RhRd_{m} = \sqrt{2Rh_{T}} + \sqrt{2Rh_{R}}

=2×64×105×18+2×64×105×32= \sqrt{2 \times 64 \times 10^{5} \times 18} + \sqrt{2 \times 64 \times 10^{5} \times 32}

=48×10210+64×10210= 48 \times 10^{2}\sqrt{10} + 64 \times 10^{2}\sqrt{10}

=112×102×10m= 112 \times 10^{2} \times \sqrt{10}m

=35417.5m=35.42km= 35417.5m = 35.42km