1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Algebra problem: walking on the surface of the earth (check if answer is correct)

  1. Mar 25, 2012 #1
    1. The problem statement, all variables and given/known data
    Arnoldo Téllez walked one mile to the south, then one mile to the east, and then one mile to the north, getting back to the point where he started. He could have started in the north pole, but he didn't. Where did he start?
    (Taken from ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY: A PROBLEM-SOLVING APPROACH, by Varberg and Fleming.)

    2. Relevant equations

    3. The attempt at a solution
    He could have started at several different points:
    - At any of the points that are one mile to the north from the parallel whose length is one mile (if that parallel exists).
    - At any of the points that are one mile to the north from the parallel whose length is one half of a mile (if that parallel exists), thus walking twice over that parallel.
    - At any of the points that are one mile to the north from the parallel whose length is one third of a mile (if that parallel exists), thus walking three times over that parallel.
    - and so on...

    Is the answer correct?
     
  2. jcsd
  3. Mar 25, 2012 #2
    Yes. The parallels specified do exist, with points available one mile to the north - where?
     
  4. Mar 25, 2012 #3
    Where?

    Those points must be part of other parallels, respectively.
     
  5. Mar 25, 2012 #4
    Sorry, I wasn't clear. Where are the parallels of the required length, given that they must also have points one mile to the north?
     
  6. Mar 25, 2012 #5
    Those parallels must be on the southern hemispere. I don't know exactly where.
     
  7. Mar 25, 2012 #6
    Where do you find such short parallels?
     
  8. Mar 25, 2012 #7
    South Pole?
     
  9. Mar 25, 2012 #8
    Near the South Pole, that is.
     
  10. Mar 25, 2012 #9
    Correct! Very near the south pole, in fact. You can essentially ignore the curvature of the Earth to get a good approximation of how far they are from the pole...
     
  11. Mar 25, 2012 #10
    The Antarctic?
     
  12. Mar 25, 2012 #11
    Arnoldo Téllez could have started at any of the points which are one mile to the north from the parallel which is at 1/(2*pi) miles from the South Pole; i.e. he could have started at any of the points which are (1 + 1/(2*pi)) miles from the South Pole.
     
  13. Mar 25, 2012 #12
    Right?
     
  14. Mar 27, 2012 #13
    Sorry analyzer - yes, absolutely correct, for the "once round the pole" version...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Algebra problem: walking on the surface of the earth (check if answer is correct)
Loading...