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Relative speed problem

  1. May 5, 2014 #1
    1. The problem statement, all variables and given/known data
    Mary sits on the perimeter of a merry-go-round undergoing uniform circular motion. Matt stands on the ground 12 m from the centre of the merry-go-round. Matt observes Mary coming towards him at a speed of 1 m/s. What is Matt's speed from the point of view of Mary?

    (Ans: 2m/s)

    2. Relevant equations



    3. The attempt at a solution
    I made a sketch according to the given problem. A denotes Mary and B denotes Matt.

    Shouldn't the answer be 1 m/s? If Matt observes Mary coming towards him with 1m/s, then Mary should also observe Matt coming towards her with 1 m/s. I don't see why this is wrong.

    Any help is appreciated. Thanks!
     

    Attached Files:

  2. jcsd
  3. May 5, 2014 #2
    Neither do I.

    Chet
     
  4. May 5, 2014 #3
    I myself wanted to dismiss the answer as wrong but considering that the problem is from a very trusted source, I couldn't. Here is the source: http://www.komal.hu/verseny/feladat.cgi?a=feladat&f=P4619&l=en

    Is my interpretation of problem correct? Would it be right to say that 1m/s is along the tangent of merry go round?
     
  5. May 5, 2014 #4
    Maybe it loses something in the translation. They are talking about speeds, not velocities. Who know's what they really meant?

    Chet
     
  6. May 5, 2014 #5
    I think you are right. Usually the translation is ok but looks like they missed it this time.

    I tried to look at the Magyar version of the website. This is the Magyar version of the problem: http://www.komal.hu/verseny/feladat.cgi?a=feladat&f=P4619&l=hu . From Google Translate, I see that they mention the radius of merry-go-round which is absent from the English version. Maybe they missed something more?
     
  7. May 5, 2014 #6
    I think they meant velocity by sebesség.

    (Szerintem a sebesség velocity lenne angolul)

    Also, I don't think that sugár is a brilliant replacement word for radius, but that's just my opinion.
     
  8. May 5, 2014 #7
    Do you know Hungarian? If so, can you please translate the problem? That would be greatly appreciated. Thanks!
     
  9. May 5, 2014 #8
    Yes I speak it fluently.

    Mari egy 6 méter sugarú, egyenletesen forgó körhinta szélén ül. Máté a körhinta középpontjától 12 méterre a földön áll. Máté úgy látja, hogy Mari éppen feléje mozog 1 m/s sebességgel. Mekkora sebességgel mozgónak látja Mari Mátét?

    Mary is on the edge of a uniformly rotating carousel with radius of 6 meters. Mate stands 12 meters away from the axis of the carousel on the ground. Mate sees as Mari approaches her with a velocity of 1 m/s. At what velocity does the motion of Máté appear to Mari?
     
  10. May 5, 2014 #9
    Thank you once again!

    So looks like the missing piece of info was the radius of merry-go-round and the velocity part. But still, I don't see why the answer should differ from 1m/s.
     
  11. May 5, 2014 #10
    I suspect that there is a Chance that the English to Hungarian translation went wrong somewhere. (the Question on the Hungarian website is taken from an American paper)
     
  12. May 5, 2014 #11
    Ah, looks like I should accept that the problem is erroneous. :(
     
  13. May 5, 2014 #12
    There are many ways for a question to go wrong. Possibly the answer of 2 on the website is a typo. Who knows?
     
  14. May 5, 2014 #13
    The problem statement is probably erroneous because I doubt they would ask such an easy problem (with answer 1m/s) for 4 points. :tongue:
     
  15. May 5, 2014 #14

    TSny

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    There's a way to get an answer of 2 m/s. Note first that Mary sits on the edge of the merry-go-round.

    What if she sat at the center of the merry-go-round? Would Mary see Matt moving at the same speed that Matt sees Mary moving?
     
  16. May 5, 2014 #15
    Why should it be different? :confused:
     
  17. May 5, 2014 #16

    TSny

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    If Mary sits at the center, then she sees Matt (and trees, houses, etc.) whirling around her.
     
  18. May 5, 2014 #17
    Ah yes, I think I see how you reach the answer of 2m/s. If I consider the angular velocity to be 6 rad/s, then Matt has a speed of 2 m/s in frame of Mary. This is probably what the question meant. Thanks TSny! :smile:
     
  19. May 5, 2014 #18

    TSny

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    6 rad/s?
     
  20. May 5, 2014 #19
    Woops, I meant 1/6 rad/s. :redface:
     
  21. May 5, 2014 #20

    TSny

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    OK. Sounds good.
     
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