An experimental fireworks shell is launched vertically from point \(A\) with an initial velocity of magnitude \(v_{0}=100 \mathrm{ft} / \mathrm{sec}\). In addition to the acceleration due to gravity, an internal thrusting mechanism causes a constant acceleration component of \(2 g\) in the \(60^{\circ}\) direction shown for the first 2 seconds of flight, after which the thruster ceases to function. Determine the maximum height \(h\) achieved, the total flight time, and the net horizontal displacement from point \(A\). Plot the entire trajectory. Neglect any acceleration due to aerodynamics.

A (28 60