Four boats are on a large lake arranged so that they form the corners of a square of edge length \(\ell = 1\text{ km}.\)

At time zero, each boat starts moving with velocity \(v_\textrm{boat} = \SI[per-mode=symbol]{10}{\kilo\meter\per\hour}\) such that its bow is always pointed directly toward its counterclockwise neighbor.

How long will the boats take to collide (in minutes)?

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