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Thread: People Moving Around Circle Track

  1. #1
    Oct 2011

    People Moving Around Circle Track

    Bob and Sally are each going for a run around a circlar track of radius 80 feet. They start running from different locations on the circle.
    Bob starts at the easternmost point and jogs 10 feet/second around the track in the clockwise direction.
    Sally runs counterclockwise at 14 feet/second and passes Bob for the first time in 16 seconds.
    (Words I bolded are the given information we need)

    Find Sally's x and y coordinates in 12 minutes.
    So here is what I'm thinking on a coordinate plan
    Bob starts at the easternmost point (meaning all the way on the right), at (80,0)
    Sally is somewhere
    Circumference: 2πr = 2π(80) = 160π feet, π is pi by the way. This is the full length track.
    Though, I'm still confused on how to start out.
    Can someone help?
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  2. #2
    Nov 2011

    Re: People Moving Around Circle Track


    Here's a blueprint to solve this problem:

    1) You may write the positions on the track as a function of an angle which varies with time because Bob and Sally are moving. Let's call this angle $\displaystyle \theta$.
    2) Find $\displaystyle \theta$ as a function of time for each runner
    3) Using the previous functions, you can use the time at which they first meet in order to find where does Sally start running

    I hope this helps
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