Q$\mathrm{.}1.(25$ Marks$)$A $1700-$kg car traveling east with a speed of $25\mathrm{.}0$ m$/$s collides at an intersection with a $2800-$kg van traveling north at a speed of $20\mathrm{.}0$ m$/$s$.$ If the vehicles undergo a perfectly inelastic collision $($that is$,$ they stick together$).$a$)$ Determine the resulting velocity and direction after the collisionTime taken for vehicles to come to a complete stop, assume Mk$=0\mathrm{.}5$ and the vehicles remain together