A small rocket is fired from a launch pad $10$ m above the ground with an initial velocity $($:$200,400,600$:$)\frac{m}{s}.$ 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$.$