$[6]3.$ Let $r(t)$ be the position of a projectile which is launched from the point $(0,0,2)$ meters at $t=0$ sec with initial velocity $($:$50,60,80$:$)\frac{m}{sec}.$ Assuming the projectile is influenced only by gravity, and that the acceleration due to gravity is $9\mathrm{.}8\frac{m}{se{c}^2},$ we have $r^{\text{'}\text{'}}(t)=($:$0,0,-9\mathrm{.}8$:$)\frac{m}{se{c}^2}.$ Find the position function $r(t),$ and the time at which the projectile will hit the $xy$ plane $($i$.$e$.$ the ground$),$ to the nearest $0\mathrm{.}01$ second.