The $230,000lb$ space$-$shuttle orbiter touches down at about $220m\frac{i}{h}r.$ At $200m\frac{i}{h}r$ its drag parachute deploys. At $35m\frac{i}{h}r,$ the chute is jettisoned from the orbiter. If the deceleration in feet per second squared during the time that the chute is deployed is $-0\mathrm{.}0003v^2($speed $v$ in feet per second$),$ determine the corresponding distance traveled by the orbiter. Assume no braking from its wheel brakes.