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> That's a surprisingly cute little puzzle, at least in the case where the
> speed of the current matches the speed of the boat and you can prove
> without any calculation that it follows a parabolic arc. In general I
> think the curve is of the rather less elegant form x*sinh(v*log(x)+c)
> where x>=0, although it's possible I made a mistake somewhere.
I started to try and figure it out using calculus but it all got too
complicated when I tried to write the velocity in terms of the current
position. I kind of guessed intuitively it would be an interesting shape, I
thought like half a water drop or something.
> Did you come up with this on your own or did you hear it elsewhere?
I came up with it on my own somehow, I don't recall how I got round to
thinking about it!
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