A $200$ g ball is thrown vertically up from the ground with an initial velocity of $25$ m$/$s$.$ The

air resistance, f $=2$ x $10^-4$

v$^2$

$($N$)$ where v is in m$/$s$.$ Determine $($a$)$ the maximum height

attained by the ball, $($b$)$ the speed of the ball when it returns to the ground, $($c$)$ the total

elapsed time.