If i threw a ball vertically at an initial speed of 34m/sec how many seconds would it take to reach it's maximum height?

The acceleration due to gravity increases the downward speed (or decreases
the upward speed) of any object that doesn't have any other forces acting on it,
by 9.81 meters per second every second.

So after a launch of 34 m/s straight up, the ball runs out of upward gas, reaches
the peak of the toss, and begins to fall, in . . .

             34 / 9.81 = 3.47 seconds .