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(A) The range $d$ of line of sight communication is given by the formula $d = \sqrt{2Rh_t} + \sqrt{2Rh_r}$,where $h_t$ is the height of the transmitti

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$\frac{h}{2}$

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(A) The range $d$ of line of sight communication is given by the formula $d = \sqrt{2Rh_t} + \sqrt{2Rh_r}$,where $h_t$ is the height of the transmitting antenna and $h_r$ is the height of the receiving antenna,and $R$ is the radius of the Earth.Given that the sum of the heights is constant,$h_t + h_r = h$,which implies $h_t = h - h_r$.Substituting this into the range formula: $d = \sqrt{2R(h - h_r)} + \sqrt{2Rh_r}$.To maximize the range $d$,we differentiate $d$ with respect to $h_r$ and set it to zero:$\frac{dd}{dh_r} = \sqrt{2R} \left( \frac{1}{2\sqrt{h - h_r}} (-1) + \frac{1}{2\sqrt{h_r}} \right) = 0$.This simplifies to $\frac{1}{\sqrt{h_r}} = \frac{1}{\sqrt{h - h_r}}$,which means $h_r = h - h_r$.Therefore,$2h_r = h$,or $h_r = \frac{h}{2}$.

If the sum of heights of transmitting and receiving antennas in line of sight communication is $h$,then the height of the receiving antenna,to have the maximum range,is

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