Solveeit Logo

Question

Question: A transmitting antenna of height 20 m and the receiving antenna of height *h* are separated by a dis...

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

45 m

Explanation

Solution

: dM=2RhR+2RhTd_{M} = \sqrt{2Rh_{R}} + \sqrt{2Rh_{T}}

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

40×103=2×6400×103×h+2×6400×103×2040 \times 10^{3} = \sqrt{2 \times 6400 \times 10^{3} \times h} + \sqrt{2 \times 6400 \times 10^{3} \times 20}

40×103=2×6400×103×h+16×10340 \times 10^{3} = \sqrt{2 \times 6400 \times 10^{3} \times h} + 16 \times 10^{3}

h=[(4016)×103]22×6.4×106=45mh = \frac{\lbrack(40 - 16) \times 10^{3}\rbrack^{2}}{2 \times 6.4 \times 10^{6}} = 45m