A small rocket is fired from a launch pad $20m$ above the ground with an initial velocity $($:$250,500,550$:$)\frac{m}{s}.$ A cross wind blowing to the north produces an acceleration of the rocket of $3\frac{m}{s^2}.$ Assume the x$-$axis points east, the $y-$axis points north, the positive z$-$axis is vertical $($opposite g$),$ and the ground is horizontal. Answer parts a through d$.$