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A crashing train

  1. Dec 12, 2011 #1
    two trains approach each other at 60m/s the gap between them is 120 m. A bird on one train flies to the other in 120m/s. The bird flies back again. But how many trips would the bird do before the trains crash?

  2. jcsd
  3. Dec 12, 2011 #2
    Is this 60 m/s the velocity of both trains relative to the earth, or relative to each other?
  4. Dec 12, 2011 #3
    What kind of bird?
  5. Dec 12, 2011 #4
    An unladen african swallow.
  6. Dec 12, 2011 #5
    An unladen African swallow's top speed is about 18 m/s. What kind of bird can fly at 120 m/s (268 mph)?
  7. Dec 12, 2011 #6
    60 m/s relative to the earth. And the type of bird doesn't matter! It just travels 120 m/s
  8. Dec 12, 2011 #7
    Some kind of birdplane? Or bird of prey in a steep dive.
  9. Dec 12, 2011 #8
    all that doesn't matter!! ok asume it is a particle which can "fly" from one of the train to the other and backforth
  10. Dec 12, 2011 #9
    Im taking a guess! Correct me if im wrong! 2 Sec's? 120 ms to 120ms back?
  11. Dec 12, 2011 #10
    by the way the trains crash 1 sec after they start their motion.
  12. Dec 12, 2011 #11
    I have done a crude from first principples method that suggests that there could be an infinite number of stops made by the bird (transit time for the bird between the trains drops exponentially). This however feels silly, and I gave up pursuing the method after I established that the bird would be landing for third time returning to its start point after 0.975 seconds while the trains were 9m apart (thats 4.5 m from the point of impact). The bird will probably be able to make a return trip over that diminished distance before the trains impact, but I havent done any work to prove so.
  13. Dec 12, 2011 #12
    have you assumed the fact that after the bird started flight the destination train gets near the bird?
    as you said infinite stops is wrong because it implies that the trains dont collide!
  14. Dec 12, 2011 #13
    Yes I have taken the motion of the trains into account. Im trying to get my head around how to come up with a raw number in a more elegant way than simply chunking it down into smaller and smaller time iterations, waiting for the bird to not have enough time to get between the 2 trains as they close. I have a gut feeling the answer is 2 complete and one incomplete transit. But cant prove it... yet.
  15. Dec 12, 2011 #14
    i came up with:

    summation of [(2)/(3)^b] equals 1.

    where b is the number of stops.
  16. Dec 12, 2011 #15
    I am not able to solve this equatio, b becomes infinity!
  17. Dec 12, 2011 #16
    Yea, which is the problem I have run into, especially if we assume the bird takes zero time to change direction - it is always moving faster than the trains and has an ever decreasing distance to cover. I tried plotting the displacement of all objects from the colission point and ended up with a nice pattern - 2 lines of constant gradient for the motion of the trains, and a line for the motion of the bird with the correct relative gradient, and simply ended up with a recursive zigzag for the bird that seemed to be going fractal. I am very tempted to actually programme this into some kind of simulation to see what should happen and work backwards...
  18. Dec 12, 2011 #17
    oh please do programme a simulation, they help a lot. I havent learnt programming.
    Can you explain what you plotted? (the gradients)?

  19. Dec 12, 2011 #18


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    Homework Helper

    Looks like a Zeno's paradox.
    The computer can't go much further without running into calculation problems with the small numbers.
  20. Dec 12, 2011 #19


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    Yes. It is simply a convergent series. It has infinite elements yet sums to a finite number.

    Same as 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... = 2.
  21. Dec 13, 2011 #20
    so what is the conclusion? does it literally mean infinity "exists"???? because afterall the trains must crash. But infinity doesnt exist
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