Boat race

[davieddy]

Originally Posted by Mr. P-1

That's a trivial special case of the problem davieddy posed, namely, when the constant speed relative to the water is exactly zero. It is trivial because, no matter how you steered the boat, it would travel along the same path and take the same time to do so.

That special case is not trivial.
A good old fashioned way of monitoring the speed of the water
is oranges.
A) you can see them
B) they don't sink
C) but only just, so wind effects are neglible.

If you place 100 along the starting line at Putney,
which one would finish first at Mortlake??

David

[davieddy]

Originally Posted by science_man_88

2 possibilities I see depend on what you say relative means.

It ain't what I say.
The understanding of "relative" is more or less the start
of undertaking conversation or geometry, let alone physics or whoremanship.

What is required is some frame of reference.

Einstein

Relative

[davieddy]

Originally Posted by Mr. P-1

http://en.wikipedia.org/wiki/Calculus_of_variations

I deliberately paused before responding to this, it being IMO about
the most beautiful thing in maths/physics. It was the reason I posed
the "puzzle" in the first place. Is there a simple way of explaining how this
type of problem is done by a computer these days?

Can one give a layman's explanation as to why the solution to
the brachistochrone and tautochrone problems is a cycloid?

David