Re: Solution to a problem!!

[Ludwik Kowalski <kowalskiL@Mail.Montclair.edu>]

John Mallinckrodt ended his critical remark with:

> Is this a convincing argument?
Well ....
John

I agree with John that part 1 of my short message was confusing. But
part 2 (see below) does not depend on this confusion. Is the "proof"
of part 2 sufficiently convincing? I was trying to show that the
solution
we found is not limited to the "fixed angle" strategy. I will think more

about this after the class.
                                            Ludwik Kowalski

> > 2) Our problem can be analyzed in a similar way. The rowing
> > velocity (in the shore's frame of reference) for any chosen
> > "fixed angle" is a straight line. We already know where the boy
> > should reach the shore to yield the shortest time (for the fixed
> > angle strategy). Then he runs toward the girl along the shore.
> > This defines a right triangle ABC, where A is the starting point
> > for the boat, B is the landing point, and C is where the girl is
> > waiting. (Please make a drawing to follow my logic.)

> > The reduction of time (from what we have already calculated)
> > is impossible if the boat turns to the right from AB because
> > both rowing and running become longer. But suppose it turns
> > left and lands at a point D which is closer to C than B (keep
> > drawing).  Can the overall time be shorten in this way? Not
> > at all. Let me prove this by "the reduction to absurdum".

> > Suppose that the overall ADC time becomes shorter than ABC.
> > Note than AD is now a curved line. Then the new time T' must
> > be compared with the ADC time T" for which AD is a straight
> > segment. Clearly T" must be shorter than T' (look at your
> > drawing). But this would contradict our previous finding
> > according to which the ABC time is shorter than the time
> > along the sides of any other right triangle.
> >
> > Is this a convincing argument?
> > Ludwik Kowalski