Problem $4.$ A ball is thrown vertically upward with an initial velocity of $10$ meters per second. Its height after t seconds is given by h$($t$)=$at$2+10$t $+1($a$)$ Find the value of a if the ball reaches its maximum height after $5$ seconds. $($b$)$ What is the maximum height the ball reaches? $($c$)$ When will the ball hit the ground? $($d$)$ How fast is the ball traveling when it hits the ground?