This motion of all can be divided in to two, first the upward motion and second downward motion.
In case of projectiles time taken for upward motion = time taken for downward motion.
So we have time taken for upward motion = 8.14/2 = 4.07 seconds
We have equation of motion, v = u+at, where v is the final velocity , u is the initial velocity, a is the acceleration and t is the time taken.
In case of upward motion
v = 0 m/s
t = 4.07 seconds
a = -9.8 [tex]m/s^2[/tex]
Substituting
[tex]0 = u - 9.8*4.07\\ \\ u = 39.886 m/s[/tex]
So initial velocity of ball = 39.886 m/s.
