## 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).

1. anonymous

I don't have a clue what this question wants exactly

2. dan815

okay

3. dan815

interesting okay, so no matter the weird speed he takes the point is he finished both journies in 12 hours

4. anonymous

Right lol

5. dan815

we have to show there is always one point such that the elevation is the same at the same time

6. dan815

ok hang on brb

7. anonymous

Yeah np

8. Astrophysics

IVT

9. ganeshie8

Just show that E(0) and E(12) have opposite signs and use IVT

10. anonymous

Intermediate Value theorem?

11. Astrophysics

Yup

12. anonymous

How do you know you have to use that tho?

13. dan815

ok back

14. dan815

now consider 2 functions h(t)

15. ganeshie8

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

|dw:1435215072294:dw|

17. dan815

you see no matter what his function of height is over time

18. dan815

there must be an intersection between h1(t) and h2(t)

19. dan815

|dw:1435215133891:dw|

20. ganeshie8

1 picture > 1000 words

21. anonymous

Right...

22. anonymous

LOL @ganeshie8

23. dan815

|dw:1435215224870:dw|

24. dan815

ya its hard to say in words lol but

25. dan815

you can see, intuitively like no matter what function u can possibly think of, this intersection must exist somewhere

26. dan815

and an intersection means the time and height was the same

27. anonymous

Correct

28. anonymous

And to prove that we gotta use the IVT?

29. ganeshie8

yeah IVT is for mathematical proof that picture is for convincing yourself why IVT works the way it does

30. anonymous

E(t) has to change signs from + to - ?

31. dan815

right, that would mean there is an intersection neat trick

32. dan815

we know that h2(0) - h1(0) = Max height and h2(12)-h1(12) = Negative of Max height

33. anonymous

hmm... how do you know that again?

34. dan815

that is what is given to us

35. anonymous

Ohhh i just realized!! Sorry my bad! >.<

36. dan815

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

Mhmm I get it now

38. ganeshie8

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

haha i like that

40. anonymous

Ahah right that makes sense lol xD nice visualization XD

41. ganeshie8

ikr! everybody likes to duplicate themselves, especially before exams so that more work can be done in less time ;p

42. ganeshie8

*likes the idea of

43. Astrophysics

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

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

Good problem though, not too difficult either just needs you to understand IVT really :P

46. anonymous

That was a perfect explanation @Astrophysics!!! And beautiful drawings too ;P

47. Astrophysics

I think what ganeshie said would work if the monk was an electron, and haha your welcome :)

48. anonymous

Thanks so much @dan815 @ganeshie8 @Astrophysics XD

49. anonymous

Hahaha electrons dont duplicate... could be DNA though :P lol

50. Astrophysics

True...but they can be in two places at once! See..at the quantum level nothing makes sense!

51. anonymous

Hahaha thats a good point :DDD

52. anonymous

Thanks again for all the help! :D

53. Astrophysics

Np, have fun studying xD

54. anonymous

Lol thanks... fun tho? XD