A toy cannon uses a spring to project a $5\mathrm{.}28-$g soft rubber ball. The spring is originally compressed by $5\mathrm{.}02$ cm and has a force constant of $8\mathrm{.}08$ N$/$m$.$ When the cannon is fired, the ball moves $15\mathrm{.}5$ cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of $0\mathrm{.}0319$ N on the ball.

$($a$)$ With what speed does the projectile leave the barrel of the cannon? $($b$)$ At what point does the ball have maximum speed?