Shoot the Monkey (Harvard Natural Sci)

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.

 

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