What happens when you shoot an arrow straight in the air?

Answer 1

An arrow shot vertically into the air will lose velocity and reverse direction. When it begins to descend, the fletching will quickly cause it to re-orient with the point downward. It will accelerate until it reaches its terminal velocity. Assuming an atmospheric density of 1.3 kg/m^3, and an arrow with a drag coefficient of 1.2, a weight of 0.23 N (200 grains), cross-sectional area of 23.48 mm^2, I calculate a terminal velocity of 112.6 m/s. That's about the same as the initial velocity when shot from a compound bow! One question remains, however: does the arrow have enough time during its descent to reach terminal velocity? That would depend on how high you shot it in the first place. Roughly speaking, though, the faster it was going when it left the bow, the faster it will be going when it reaches the ground.