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A TV transmitting antenna is 128 m tall....

A TV transmitting antenna is 128 m tall. If the receiving antenna is at the ground level, the maximum distance between them for satisfactory communication in line of sight mode is (radius of the earth `6.4 xx10^(6)` m)

A

`64 xxsqrt(10) km`

B

`128/sqrt(10) km`

C

`128xxsqrt(10) km`

D

`64/sqrt(10) km`

Text Solution

Verified by Experts

The correct Answer is:
b
Maximum distance between transmitting and receiving antenna is given by,
`d= sqrt(2R_(e)h_(r))`
`= sqrt(2xx6.4xx10^(6)x128)`
`d = 128 xx10^(2)sqrt(10) m`
On multiplying and dividing by `sqrt(10)`,
` implies d=(128xx10^(2)sqrt(10))/sqrt(10)xxsqrt(10)`
` therefore d=128/sqrt(10) km`.
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