Answer
Please see the work below.
Work Step by Step
We know that the range is given as
$R=\frac{(v_{\circ})^2}{g}$
This simplifies to:
$v_{\circ}=\sqrt{Rg}$
The maximum altitude is given as
$y=\frac{(v_{\circ})^2}{2g}=\frac{Rg}{2g}$
$y=\frac{R}{2}$
We plug in the known values to obtain:
$y=\frac{180Km}{2}=90Km$
