soap opera box

[kowalskil@alpha.montclair.edu]

I got two clarifications (in private) and they point to the ambiguity in
the original formulation of the problem (see below).

R. wrote:

> Took me a while to recognize what was going on.  The key here is that
> the rope doesn't expand by 1 km in front of the worm but rather by 1 km
> overall. 

Yes, the speed of the tractor is 10,000 cm/s. Two objects are in motion
and the algorithms for the distance versus time are specified in words.
I do not care about the elestic rope at all. The question was "will the
two moving points meet or not"? Will the turtle ever catch Achilles? 
Of course not, unless he runs slower than the turtle.

And S. wrote:

> No, the worm's 1 cm/s is w/respect to the rope...so if he were at the half
> way point, his speed relative to the ground would be 1 cm/s + (1/2) 1 km/s.

HERE IS THE ORIGINAL WORDING BY LEIGH:

> At time t=0 a worm starts to crawl from one end of the rope to the other 
> at a speed of one centimeter per second. The rope itself is attached to a 
> tractor which is stretching the rope at a rate of one kilometer per second. 
> The problem as it was originally stated specifies that the rope lengthens 
> by one kilometer at the end of each second, and it is this discrete version
> of the problem I will continue with here. At the end of one second the worm
> has marched one centimeter toward the other end of the rope. At that
> instant he is instantaneously transported to the 2 centimeter mark on a
> rope which is now two kilometers in length. By calculation you will see
> that at the end of the second second he will be three centimeters along
> his way on the two kilometer rope, which will then lengthen to three
> kilometers, ...


Nowhere do I see that 1 cm/s is with respect to a stretching ruller. 
Kinematic problems are usually formualted in fixed frames of reference. 
Are you testing me with a "guess what I have in mind" question, Leigh? 
Did you mean that the machanism of crawling implies "v with respect to 
stretching rope"? 
                                                 Ludwik Kowalski