Odysseus' Return

Classical Mechanics Level 4

Odysseus on his ten year return voyage to Ithaca sailed between two monsters. On one side, the creature Charybdis periodically sucked the oceans such that a whirlpool formed. On the opposing side the creature Scylla would lunge down from above and devour one sailor in each of her many mouths.

Odysseus opted to sail near Scylla skirting Charybdis by 500 m. At this distance, the maximum drop in water level of the ocean was 0.2 m from between when Charybdis was draining the oceans and when he was not. At Charybdis' mouth the funnel of the whirlpool is 25 m wide. Assume that the oceans are perfectly calm and that there are no intermolecular attractions between water molecules.

How deep is Charybdis under water?

Note: This problem was originally proposed by Brian Yue for the IPhOO.


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