What is its time interval between the release
of the ball and the time it reaches its
maximum height? the acceleration of gravity
is 9.8 m/s
2
and the maximum height is 3.8 m .

There are several many equations that are available to relate the distance,
speed, and time of a body moving vertically in gravity.  Happily, the only one
I can always remember without looking it up happens to be the right one to
use for this question !

             Distance  =  (1/2) x (gravity) x (time)²

                   3.8 m  =  (1/2) x (9.8 m/s²) x (time)²

Divide each side
by 4.9 m/s² :

                   (3.8 m) / (4.9 m/sec²)  =  (time)²

                     0.7755  sec²  =  time²

Square root
of each side:

                       0.88 second  =  time