Question
The monkey falls off the tree the exact instant the shot is fired. So, to hit the falling monkey exactly, should you aim your shot exactly at the monkey, or slightly below? (Assume air resistance is negligible)
Answer:
You should aim exactly at the monkey (assuming air resistance is negligible).
Yes, the monkey is falling. But so is the bullet!
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. At any time, the deviation from the zero-gravity-straight-line path is a vertical distance of 0.5gt2. What about the moneky? It would also 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.
xmPhysics 