$1$ Problem

A fighter jet at the Cherry Point airshow performs a vertical constant$-$radius loop maneuver as sketched below. As it begins the maneuver at the point shown below $($point $P)$ the aircraft's total acceleration is $3$ g and the airspeed is $800k\frac{m}{h}$ and increasing at a rate of $20\frac{k\frac{m}{h}}{s}=5\mathrm{.}556\frac{m}{s^2}($along the loop$).$ Determine the radius of the vertical loop.