The puzzle. This is the classic “monkey and hunter” problem, with a treat instead of a banana. A zookeeper aims a banana launcher straight at a monkey hanging from a branch. At the instant the banana is launched, the monkey lets go of the branch. Gravity pulls the banana down below the line it was aimed along. Surprisingly, the monkey still catches the banana.

Two independent motions. Horizontal and vertical motion can be treated separately. With no air resistance, nothing changes the banana's horizontal velocity, so it reaches the tree at a steady rate. Vertically, the banana and the monkey both accelerate downwards at g.

Why it works. Without gravity the banana would travel along the aim line straight to the monkey, and the monkey would stay where it is. Gravity makes each of them fall the same distance, ½gt², below where they would otherwise be. So when the banana reaches the tree, it is the same distance below the aim line as the monkey is below the branch, and they meet.

Any speed. A faster banana reaches the tree sooner, so both have fallen less, but they still meet. A slower banana takes longer, so both fall further, but they still meet. The only way to miss when aiming straight at the monkey is for the banana to be so slow that it reaches the ground before it gets to the tree.

If the monkey holds on. The banana still falls below the aim line, but the monkey stays put, so the banana passes underneath. To reach a monkey that holds on, the zookeeper has to aim above it by the distance the banana will fall.

In the lab. This is often shown with a tin can held up by an electromagnet. The ball leaving the launcher breaks the circuit, so the can drops at the same instant, and the ball still hits it.