A young woman in the flag corps throws her flag 2.1 meters into the air. How fast was the flag moving when she released it? How long was the flag in the air before she caught it again?

Conservation of energy tells us that:

Vo^2/2 = g*H
H = 2.1 m
Solve for Vo

Time in the air = 2 Vo/g
(Vo/g going up and Vo/g coming back down)