A cannon shoots a ball at an angle $$theta above the horizontal ground. $$

$($a$)$ Neglecting air resistance, use Newton's second law to find the ball's position as a function of time. $($Use axes with x measured horizontally and y vertically.$)$

$($b$)$ Let r$($t$)$ denote the ball's distance from the cannon. What is the largest possible value of $$theta ifr $$phi is to increase throughout the ball's flight? $[$Hint: $Ú$sing your solution to part $($a$)$ you can write down r$2$ as x$22,$ and then find the condition that r$3$s always increasing.$]$