After you posted mean things online about Aquaman, he found out where you lived and kidnapped you (using his awesome aqua-powers), taking you to his super-secret aqua-lair. He has placed you in a room with a ceiling less than $10$ feet tall, a perfectly level floor, and, at the end of the room, a perfectly vertical wall with a mark exactly $5$ feet above floor level. There is a drain in the floor so that water drained into the room will not accumulate (at all). The room is otherwise featureless. Behind the marked wall is a reservoir of water. You have access to a compass (which can only draw circles around a given center), a plumb bob (which can only indicate a perfectly vertical line), and an awl (which can only poke holes through the wall). All the walls, ceiling, and floor are all opaque and you cannot see the reservoir. Notice that the tools given do not allow you to make any measurement.
Aquaman has challenged you
If you can drain the reservoir such that its water level is exactly $10$ feet above the floor, I will return you to your house and we can forget this ever happened. Otherwise, I will get a real superhero to come and deal with you - and you don't want that!
How can you use the three tools given to drain the reservoir and to know exactly when its water level is $10$ feet above the floor?
Answer
Set the compass to some size, less than the distance from the 5ft mark to the ceiling. Use the bob to find two points on the circle, one directly above the other. Then use the awl to punch holes at these points. Wait until the streams from both holes fall on the same spot. You're done! Plug the holes in a hurry and mock Aquaman some more.
Explanation: the velocity of a stream from a given hole will be $v=\sqrt{2gd}$ where d is the distance to the top of the water. The time to fall from a height h is given by $t=\sqrt{\frac{2h}{g}}$. This means that the horizontal distance traveled by a stream before fitting the ground will be $vt=2\sqrt{hd}$.
Given that $h+d=l$ where l is the height of water above the floor, the only time $h_1d_1=h_2d_2$ is when $h_1=d_2, h_2=d_1$, which means $l=h_1+h_2$. Because the holes are symmetric about the 5ft (height) line, $h_1+h_2=10ft, l=10ft$
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