A ball is thrown vertically upward from ground level with an initial velocity of $96$ feet per second. Assume the acceleration of the ball is a$($t$)=32$ feet per second per second. $($Neglect air resistance.$)$

$($a$)$ How long $($in seconds$)$ will it take the ball to rise to its maximum height?

What is the maximum height $($in feet$)?$

$($b$)$After how many seconds is the velocity of the ball one$-$half the initial velocity?

$($c$)$What is the height $($in feet$)$ of the ball when its velocity is one$-$half the initial velocity?