Re: [Phys-l] C & C Trajectories

[Bernard Cleyet <bernardcleyet@redshift.com>]

IIRC the theorem proves it's possible to have an inverted pendulum  
stay inverted when mounted on a track and moved from one end to the  
other.  This is from a Scientific American article (or the maths  
section) of the 60's?

bc doesn't remember the theorem just the app. and maybe not even that!


"A congruent problem of a monk who traveled up a mountain and back
down - was used in my intro calculus class as an example of the Mean
Value Theorem and it's wide ranging power."   [C. Britton]


On 2008, Jun 21, , at 13:49, Richard L. Bowman wrote:

> First I thought the question was when would they pass the same  
> location at the same time, and there is not enough information for  
> that. But there is a 100% probability of such an incident  
> occurring. A distance-time graph shows that when this occurs is  
> dependent upon the velocity history of the car in both journeys,  
> but it also shows that it will always occur.
>
> Richard L. Bowman
> Bridgewater College, VA, USA
> ________________________________________
> Brian Whatcott [betwys1@sbcglobal.net] wrote on Saturday, June 21,  
> 2008:
>
> Click and Clack offered a version of the following puzzler
> this morning.
>
> A family of four drove up the west coast 400 miles on Saturday,
> starting at 8 a.m. They arrived at their destination at 4 p.m.
> Three of them returned home the following day by the same route,
>   in the same car, starting at 11 a.m. Sunday.
>
> The question: what is the probability that the car passed the
> same spot at the same time of day, going both ways?
> I was surprised that the answer was not immediately obvious.
> To me at least.
> The idea of space time diagrams came to mind.
>
>
> Brian Whatcott    Altus OK    Eureka!