ere is the position function for projectile motion on Earth $($g $=9\mathrm{.}8[$m$/$s$2]).$

r$($t$)=$

x$0+$ v$0$cos$($$)$ t$,$ y$0+$ v$0$sin$($$)$ t $4\mathrm{.}9$t$2$

Suppose that a ball is thrown with an initial position of $($x$0,$ y$0)=(0,3),$ and an initial

velocity defined by v$0=8[$m$/$s$]$ and $=45.$

$($a$)[4$ Points$]$ Find the associated velocity function, v$($t$),$ and acceleration function, a$($t$).$

$($b$)[4$ Points$]$ Find the value of t which corresponds to the highest altitude of the ball.