Minggu, 18 September 2022

Can You Solve the Jetpack Splashdown Riddle?

The Problem

It's the near future, and everyone is about to have the opportunity to fly their own jetpack. But before that can happen, a test pilot must write the safety guide for what to do in an emergency—like when the fuel gauge on the jetpack approaches zero.

In his test, the pilot hovers 100 feet above a pool of water, draining the jetpack's fuel until there's only enough left for one final moment of upwards thrust. As the pilot begins to fall, he is left with one very important question:

At what point during the pilot's fall should he activate that last bit of fuel to best minimize his upcoming splashdown velocity?

The Hint

While your intuition for what to do in this situation could carry you a long way, the mechanics of a sustained jetpack thrust also get complicated quickly. To make this easier, let's treat it like a double jump in a video game and say that the jetpack translates to an immediate change in vertical thrust that lasts for the blink of an eye.

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