A small rocket is fired from a launch pad $10$ m above the ground with an initial velocity 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.

What is expected:

$-$find the velocity vector

$-$find the position vector

$-$find the trajectory of the rocket represented by a graph

$-$find the time of flight $($seconds$)$

$-$find the range of rocket $($meters$)$

$-$find the maximum height of the rocket $($meters$)$

DO NOT ROUND ANSWERS, give answer to $4$ decimal places