> I'm not sure what you mean by a discontinuous system, but here's what happens. You find the function that gives the total amount of water hitting you as a function f(A,V) as a function of V with fixed angle A, and then try varying the parameter A. If I set it up so that negative values of A represented the rain going in the same direction as you, then there is a discontinuity of sorts when you hit negative values of A. For negative A, f(A,V) has a corner at V = R Sin(A). It's still continuous, just not differentiable at that one point, so it's the derivative that has a discontinuity. And it IS a global minimum as well as a local one, since to the right of this point f(A,V) is increasing as a function of V (though it levels off to a horizontal asymptote).
>
> You're right to say that for the walker, standing still relative to the horizontal minimizes the raindrops hitting you per second. However, if the rain were coming in from ahead, you'd have to move backward for this to happen and you'd never reach your goal. That's the main difference.

Cool. This is exactly what I was getting at. Oddly enough, though, your description this time around was vivid enough to put a rough plot of the function in my head, at least at some key points.

I'm mainly just glad that I remembered enough math to convey my query to you in a fashion that allowed you to explain the answer to me, and have it be the answer I was looking for. :-)