tag:blogger.com,1999:blog-8807287158334608095.post6876322152663681058..comments2024-03-28T11:22:03.762-04:00Comments on The Virtuosi: Problem of the Week #2Alemihttp://www.blogger.com/profile/15394732652049740436noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-8807287158334608095.post-69980703603543763172010-11-22T13:14:08.835-05:002010-11-22T13:14:08.835-05:00Re: Anonymous at Nov 21
Wow. I like your argumen...Re: Anonymous at Nov 21<br /><br />Wow. I like your argument a lot. Much more than the differential equations I used.<br /><br />The details are a teensy bit off: the acceleration of the ant is not constant, so his position doesn't vary as t^2. But, because he is undergoing SOME acceleration, his position will go as some power of t greater than 1, which - as you elegantly point out - will always beat t^1 for sufficiently large t.Anonymous Cowardnoreply@blogger.comtag:blogger.com,1999:blog-8807287158334608095.post-90016601315598854652010-11-21T19:41:18.291-05:002010-11-21T19:41:18.291-05:00The end of the rubber band is moving at a constant...The end of the rubber band is moving at a constant speed. The ant is accelerating. The position of the ned of the band varies with t, while the position of the ant varies with t^2. t^2 > t for large t. The ant always wins.<br /><br /> --CharlesAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-8807287158334608095.post-77109521134935497322010-11-15T19:51:10.144-05:002010-11-15T19:51:10.144-05:00@Anon. Coward 8:20
what differential equation did ...@Anon. Coward 8:20<br />what differential equation did you use?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8807287158334608095.post-40241126815313043572010-11-14T21:21:15.184-05:002010-11-14T21:21:15.184-05:00Thanks ants.
Thants.Thanks ants.<br /><br />Thants.Corkyhttps://www.blogger.com/profile/08035182065579585523noreply@blogger.comtag:blogger.com,1999:blog-8807287158334608095.post-66029841352180561992010-11-14T21:11:46.315-05:002010-11-14T21:11:46.315-05:00How come ants?How come ants?Bohnhttps://www.blogger.com/profile/17960046202717038304noreply@blogger.comtag:blogger.com,1999:blog-8807287158334608095.post-28631525026678079172010-11-14T20:20:02.995-05:002010-11-14T20:20:02.995-05:00Assuming that the ant is a point and always moving...Assuming that the ant is a point and always moving at a velocity v with respect to where its feet are touching...<br /><br />Brute-force solving the differential equation gives me <br /><br />t = (L/v) * ( Exp[v/u] - 1)<br /><br />So the ant always makes it to the end of the band!<br /><br />In the limit that v->0, this returns the expected result that t = L/u.<br /><br />In the limit that v >> u, the time it takes is blowing up (approximately) exponentially fast in v. It makes sense to me that the ant would always finish, but that as v>>u it would take a mighty long time.<br /><br />That it would have this specific functional form isn't obvious to me, but maybe there's a more clever way than just solving the diff-eq.Anonymous Cowardnoreply@blogger.com