Question

If the sum of the height of transmitting and receiving antenna in $LOS$ communication $10$ fixed at small $h$,show that the range is maximum has a height $\frac{h}{2}$ each?

Answer 1

$h_T+h_R=h$
$d_M=d_T+d_R=\sqrt{2R{h}_T}+\sqrt{2R{h}_R}$
$d_m=\sqrt{2R{h}_T}+\sqrt{2R(h-h_T}$
$\frac{d\left(d_m\right)}{d{h}_T}=0$
$\frac{1}{2\sqrt{h_T}}+\frac{1(-1)}{2\sqrt{h-h_T}}=0$
$\frac{1}{\sqrt{h_T}}=\frac{1}{\sqrt{h-h_T}}$
$h_T=h-h_T$
$2h_T=h$
$h_T=\frac{h}{2}=h_R$