16 Oct, 10 tweets, 2 min read
Lots of really creative answers to the "what is the optimal size rock to maximize distance" interview question, but this was the first one I saw that hit the main points the most concisely.
(1/9) I love this question because there’s so many layers and it seems simple, then complicated but then simple again once you boil it down to engineering first principles.

(2/9) The first thing to realize is that how fast the rock is moving when it leaves your hand is what matters the most here. The faster you throw the the same rock the farther it will go. FULL STOP. Seems obvious but it's a critical observation.
(3/9) Drag from the air is the other consideration here and for now just know the heavier the rock the less affected it will be. So how do find the sweet spot for maximizing the rock speed but also maximizing how heavy the rock is (they work against each other)?
(4/9) You can think about every arm as having a terminal velocity (how fast your arm can swing w/o holding anything). If you throw a feather or a pebble you will reach your personal arm terminal velocity really fast. BUT if you throw a bowling ball you will never reach it.
(5/9) So somewhere between a pebble and a bowling ball there is a perfect rock where you reach your arm terminal velocity RIGHT AS you go to release the rock. That's your max speed with the heaviest rock.
(6/9) Ignoring gravity, (because it affects all rock sizes the same), once airborne the only force acting on the rock is drag from air resistance. Turns out bumping into so many air molecules and pushing them out of the way slows you down.
(7/9) So the smaller your cross sectional area the fewer air molecules you have to bump and the less you will be slowed. Additionally, the higher your mass the more inertia you have and the less you will be slowed (eg. it's harder to stop a 1mph train vs a 1mph tricycle).
(8/9) Maximizing rock density is smart way to look at it because it generally tackles both those with one parameter.

This is a general solution (i.e. it applies to all arms regardless of size) based on engineering first principles.
(9/9) Thinking this way makes you a much more effective engineer. I wouldn't say there was one perfect answer but it was more of a way to gauge if the applicant approached engineering problems in this manner. Just like HS physics, always start with the free body diagram :)

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