JEE Main · 2021 · 31 Aug 2021 · Shift 1 · EM Waves

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If the sum of the heights of transmitting and receiving antennas in the line of sight of communication is fixed at 160 m, then the maximum range of LOS communication is ______ km. (Take radius of Earth

= 6400 km

)

Answer: 64

Solution

The line-of-sight range is

d = 2 R h_{T} + 2 R h_{R}

with the sum

h_{T} + h_{R} = 160

m fixed. Because the square-root function is concave, this sum is greatest when the two heights are equal,

h_{T} = h_{R} = 80

m. Then

d = 2 2 R h = 2 2 \times 6400 \times 1 0^{3} \times 80 = 2 1.024 \times 1 0^{9} = 2 \times 3.2 \times 1 0^{4} m .

The maximum range is

64

km.

JEE Main · 2021 · 31 Aug 2021 · Shift 1 · Integer answer

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