The key to understanding this puzzle is to realize that both the projectile motion of the bullet and the vertical fall of the monkey have the same exact acceleration (9.81 m s-2 downward).
Let’s start off by pretending that there is no gravity. By aiming at the monkey directly, the bullet would have travelled along a straight line, and the monkey would have hovered in the air, resulting in a hit.
Now let’s switch gravity back on. The bullet would now travel in a parabolic path, falling below the zero-gravity-straight-line path by a distance of 0.5gt2. The monkey would have fallen down by a distance of 0.5gt2. Because gravity affected both motions equally, gravity or not, the monkey is doomed to be hit.
xmDemo 