If the relation is H = 30t 2-5t, the opening is upward, so it is impossible to appear and there is no solution.
If the relation is h = 30t-5t 2, the opening is downward and there is a solution.
h=5t(6t- 1)=0
t 1=0 t2= 1/6
When t = (t1+t2)/2 =112s, the maximum value is taken.
H = 355/144m