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Vectors Homework

  1. Sep 17, 2016 #1
    1. The problem statement, all variables and given/known data
    You go to an amusement park with your friend Betty, who wants to ride the 90-m-diameter Ferris wheel. She starts the ride at the lowest point of a wheel that, as you face it, rotates counterclockwise.

    What is the magnitude of her displacement vector when the wheel has rotated by an angle of 80 ∘?
    and
    What is the direction of her displacement vector when the wheel has rotated by an angle of80 ∘, measured counterclockwise from the horizontal?
    2. Relevant equations
    I have no idea how to do this.

    3. The attempt at a solution
    I tried doing 45tan(80), but its gives me a wrong answer.
     
  2. jcsd
  3. Sep 17, 2016 #2
    You are comparing two points in a circle of radius 45 m (take the centre of the wheel to be the origin). Write their Cartesian coordinates and take the difference: that will be your displacement vector.
     
  4. Sep 17, 2016 #3

    TSny

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    My hint would be to draw a sketch of the situation. In the sketch, show the Ferris wheel, the displacement vector, and the 80o angle.

    You can use the sketch as an aid to carrying out Lucas' approach. Or, you might be able to get the magnitude of the displacement with a little trig applied to the sketch.
     
  5. Sep 17, 2016 #4
    Yes, I am trying to do it with trig, but it seems to give me a wrong answer?
     
  6. Sep 17, 2016 #5
    Can you guys show me how to do it with trig? I feel like I'm just stuck.
     
  7. Sep 17, 2016 #6
    Consider the triangle with the following vertices: the centre of the wheel, Betty's initial point and Betty's final point. You know one of the angles and you know two of the side lengths. Note that it is not a right angle triangle.

    If you make a sketch of this triangle and use some trig knowledge you should be able to find the magnitude.
     
  8. Sep 17, 2016 #7
    I keep getting √(52.8)^2+(44)^2 = 69 , but it's telling me im wrong ??? I added both of the vectors's components...
     
  9. Sep 17, 2016 #8
    which vectors?
     
  10. Sep 17, 2016 #9
    The (0,45) and (7.8,44) calculated from trig
     
  11. Sep 17, 2016 #10

    TSny

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    Can you describe what the first vector (0, 45) represents? Is it the vector drawn from the initial location of Betty to the center of the Ferris wheel?
    Likewise, what does the vector (7.8,44) represent?
     
  12. Sep 17, 2016 #11
    Adding these components should give the right displacement vector. I think you messed up on adding the components, so you got the wrong magnitude.
     
  13. Sep 17, 2016 #12

    TSny

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    Check to see if you might have the x and y components interchanged in (7.8, 44) and check the signs of the components.
     
  14. Sep 18, 2016 #13
    Toss Cartesia.

    A line joining two points on a circle is called a chord. The length of a chord can be determined by joining the two endpoints to the center of the circle - thus forming an isosceles triangle - and applying some trigonometry.
     
    Last edited: Sep 18, 2016
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