On 11/30/2010 8:31 AM, scott wrote:
> Maybe some of you remember the problem from basic vector math class,
> where a boat must travel across a flowing river to a certain point, and
> you need to calculate which direction the boat should point.
>
> The captain of a certain boat is not so clever though, and just aims his
> boat straight at the destination, of course the boat starts to get
> pushed off course by the river current, but the captain keeps the boat
> pointed at the destination at all times. Eventually (assuming the boat
> can overcome the river current) the boat reaches the destination. What
> shape curve did the boat trace out?
>

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.  Did you 
come up with this on your own or did you hear it elsewhere?

Post a reply to this message