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anonymous

  • one year ago

A Tibetan monk leaves the monastery at 7:00 am and takes his usual path to the top of the mountain, arriving at 7:00 pm. The following morning, he starts at 7:00 am at the top and takes another path back to the monastery, arriving at 7:00 pm. Show that there is some elevation that he reaches at the exact same time on both days. Hint: Let h1(t) be the monk’s elevation on the first day and h2(t) his elevation on the following day. Consider the function E(t) = h1(t) − h2(t).

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  1. anonymous
    • one year ago
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    I don't have a clue what this question wants exactly

  2. dan815
    • one year ago
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    okay

  3. dan815
    • one year ago
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    interesting okay, so no matter the weird speed he takes the point is he finished both journies in 12 hours

  4. anonymous
    • one year ago
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    Right lol

  5. dan815
    • one year ago
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    we have to show there is always one point such that the elevation is the same at the same time

  6. dan815
    • one year ago
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    ok hang on brb

  7. anonymous
    • one year ago
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    Yeah np

  8. Astrophysics
    • one year ago
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    IVT

  9. ganeshie8
    • one year ago
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    Just show that E(0) and E(12) have opposite signs and use IVT

  10. anonymous
    • one year ago
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    Intermediate Value theorem?

  11. Astrophysics
    • one year ago
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    Yup

  12. anonymous
    • one year ago
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    How do you know you have to use that tho?

  13. dan815
    • one year ago
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    ok back

  14. dan815
    • one year ago
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    now consider 2 functions h(t)

  15. ganeshie8
    • one year ago
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    its bit hard to accept that there exists such a time where the elevations will be equal tho also was wondering what if if the monk knows teleportation..

  16. dan815
    • one year ago
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    |dw:1435215072294:dw|

  17. dan815
    • one year ago
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    you see no matter what his function of height is over time

  18. dan815
    • one year ago
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    there must be an intersection between h1(t) and h2(t)

  19. dan815
    • one year ago
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    |dw:1435215133891:dw|

  20. ganeshie8
    • one year ago
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    1 picture > 1000 words

  21. anonymous
    • one year ago
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    Right...

  22. anonymous
    • one year ago
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    LOL @ganeshie8

  23. dan815
    • one year ago
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    |dw:1435215224870:dw|

  24. dan815
    • one year ago
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    ya its hard to say in words lol but

  25. dan815
    • one year ago
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    you can see, intuitively like no matter what function u can possibly think of, this intersection must exist somewhere

  26. dan815
    • one year ago
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    and an intersection means the time and height was the same

  27. anonymous
    • one year ago
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    Correct

  28. anonymous
    • one year ago
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    And to prove that we gotta use the IVT?

  29. ganeshie8
    • one year ago
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    yeah IVT is for mathematical proof that picture is for convincing yourself why IVT works the way it does

  30. anonymous
    • one year ago
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    E(t) has to change signs from + to - ?

  31. dan815
    • one year ago
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    right, that would mean there is an intersection neat trick

  32. dan815
    • one year ago
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    we know that h2(0) - h1(0) = Max height and h2(12)-h1(12) = Negative of Max height

  33. anonymous
    • one year ago
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    hmm... how do you know that again?

  34. dan815
    • one year ago
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    that is what is given to us

  35. anonymous
    • one year ago
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    Ohhh i just realized!! Sorry my bad! >.<

  36. dan815
    • one year ago
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    we have 2 functions h1(t) at t=0 , height is 0, t=12 hours height is max h2(t) at t=0, height is max, t=12 hours height is 0

  37. anonymous
    • one year ago
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    Mhmm I get it now

  38. ganeshie8
    • one year ago
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    Another way to visulaize it is... assume that this monk knows magic and duplicated himself - one copy starts frm bottom and the other copy starts from top at the same time; since they both are walking towards each other on the same road, they will meet at some place for sure, no matter what their individual speeds are.

  39. dan815
    • one year ago
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    haha i like that

  40. anonymous
    • one year ago
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    Ahah right that makes sense lol xD nice visualization XD

  41. ganeshie8
    • one year ago
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    ikr! everybody likes to duplicate themselves, especially before exams so that more work can be done in less time ;p

  42. ganeshie8
    • one year ago
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    *likes the idea of

  43. Astrophysics
    • one year ago
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    I think you may also need some help on knowing what exactly IVT is, so suppose f is continuous on [a.b] and let N be in (f(a),f(b)), where f(a) cannot = f(b). Then there exists a number c in (a,b), such that f(c) = N. Looks like bunch of mumbo jumbo so I'll draw a pic won't be as beautiful as dans drawing ;) |dw:1435215756830:dw| also if f(a) is negative and f(b) is positive (vice versa), then the equation f(x) = 0 has at least one root in (a,b). |dw:1435215895403:dw| hope that gives you an idea what is going on and you can relate this with your question now xD

  44. anonymous
    • one year ago
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    Oh tell me about it!! Hahaha >.< I wish I had an extra week!! Lol might pull an all-nighter tonight :( which is the worst idea ever!!

  45. Astrophysics
    • one year ago
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    Good problem though, not too difficult either just needs you to understand IVT really :P

  46. anonymous
    • one year ago
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    That was a perfect explanation @Astrophysics!!! And beautiful drawings too ;P

  47. Astrophysics
    • one year ago
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    I think what ganeshie said would work if the monk was an electron, and haha your welcome :)

  48. anonymous
    • one year ago
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    Thanks so much @dan815 @ganeshie8 @Astrophysics XD

  49. anonymous
    • one year ago
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    Hahaha electrons dont duplicate... could be DNA though :P lol

  50. Astrophysics
    • one year ago
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    True...but they can be in two places at once! See..at the quantum level nothing makes sense!

  51. anonymous
    • one year ago
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    Hahaha thats a good point :DDD

  52. anonymous
    • one year ago
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    Thanks again for all the help! :D

  53. Astrophysics
    • one year ago
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    Np, have fun studying xD

  54. anonymous
    • one year ago
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    Lol thanks... fun tho? XD

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