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The sum of the heights of transmitting a...

The sum of the heights of transmitting and receiving attennas in line of sight of communication is fixed at h, find the height of two antennas when r ange is maximum.

A

`h//2`

B

2h

C

h

D

4h

Text Solution

Verified by Experts

The correct Answer is:
A
The range of line-of-sight communication between two antennas is given by
`v=sqrt(2Rh_(T))+sqrt(2Rh_(R))`
Given `h_(T)+h_(R)=h` and let `h_(T)=H`, then `h_(R)=h-H`
`therefore r=sqrt(2R)[sqrt(H)+sqrt(h-H)]`
For r to be maximum,
`(dr)/(dH)=sqrt(2R)[(1)/(2sqrt(H))+(1)/(2sqrt(h-H)(-1))]=0`
or `(1)/(2sqrt(H))-(1)/(2sqrt(h-H))=0` or `H=h-H` or `H=(h)/(2)`
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