> 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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