1.

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.

Answer»

`h//2`
2h
h
4h

Solution :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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