Bird Flies Between Two Trains Crashing at 60m/s

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Homework Help Overview

The problem involves two trains approaching each other at a speed of 60 m/s with a gap of 120 m between them, while a bird flies back and forth between the trains at a speed of 120 m/s. The question posed is how many trips the bird can make before the trains collide.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relative speeds of the trains and the bird, question the type of bird, and explore the implications of infinite trips versus finite time until collision. Some participants attempt to derive mathematical expressions related to the problem.

Discussion Status

The discussion is ongoing, with various interpretations being explored. Some participants have provided mathematical insights and conjectures about the number of trips the bird can make, while others question the assumptions made regarding the bird's behavior and the nature of the problem itself.

Contextual Notes

There are assumptions about the bird's instantaneous change in direction and its mass, which are being debated. The discussion also touches on concepts like Zeno's paradox and convergent series, indicating a philosophical dimension to the problem.

  • #31
neutrino' said:
so it isn't conclusive proof that infinity exists? I mean the trains crash but how come the particle (the bird with ~0 mass) make inifintely many stops? THE TRAINS CRASH, RIGHT??

Once we add in assumptions that the particle has no dimensions, nor mass - so that the train don't both contact the particle until the trains are also touching each other - and the particle ca also change from velocity in one direction to velocity in the other direction [ie have infinite acceleration] it is not surprising that the number of trips the particle makes in infinite - but then only the first half of the infinite trips took any real time - the rest of them were done in an infinitely small time interval, perhaps?
 
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  • #32
neutrino' said:
so it isn't conclusive proof that infinity exists?

What does one man by "exist"? Is it a useful tool in mathematics? Absolutely. We just used it in one.

Does it exist in some physical way? This experiment gets us no closer to an answer, since this is so clearly an unphysical thought experiment (zero mass, point-sized birds and such).
 

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