when we hit the ball we transfer energy from bat to the ball , and within ball its energy is kinetic energy, when it goes up into the air its potential energy become increasing and so its kinetic will decrease according to conservation of energy and eventually it is zero at this moment potential energy is maximum so the height is also maximum.
0.5m v^2 = mgh
0.5 *16*16 = 9.8* h
so h = 1.33 m
as the motion is kinetic motion in one dimensional
so, time to go maximum height , t1
as, v= u+at here a= -g because acceleration is acceleration due to gravity which always act downward
v=0 at maximum height
so t1 = u/g = 16/9.8 = 1.63 s
as the time taken to reach maximum height is equal to time taken to come back to ground from maximum height.