Answer:
The easiest way to do this is to realize that the time to fall is the same as the rise time (conservation of energy can easily verify this)
S = 1/2 g t^2 time to fall 2.5 m
t = (5 / 9.8)^1.2 = .714 sec time in air
v = a t = 9.8 * .714 = 7 m/s initial vertical speed
Check:
S = v t - 1/2 g t^2 where v is the initial vertical speed
S = 7 * .714 - 4.9 * .714^2 = 2.5 m total vertical distance traveled
