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Math Help - equations of circles trig

  1. #1
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    equations of circles trig

    I need to know how to solve a problem like this on my final tomorrow and I don't know how, please help!




    So there's a ferris wheel. The bottom is say 5 feet off the ground. It has a radius of 10 feet. It turns 1 degree every second.

    How would I write this wheel's equation?? like how to find the height for time "t"

    I don't even know where to start...
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  2. #2
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    Hello, pyrosilver!

    So there's a ferris wheel. The bottom is say 5 feet off the ground.
    It has a radius of 10 feet. It turns 1 degree every second.
    There is no "wheel's equation".

    But we can express the height of a "car" at time t.
    Code:
                  * * *
              *           *
            *               *
           *                 *
    
          *         O         *
          *         *         *
          *   10  *t|         *
                *   |
           *  *     |        *
          A * - - - *B      *
            : *     |     *
            :     * * *
          h :      C|
            :       | 5
            :       |
      - - - * - - - * - - - - - -
            E       D

    The center of the wheel is at O.
    Its radius is: OA = OC = 10.
    "The bottom is 5 feet off the ground": CD = 5,\;OD = 15

    The car is at A.
    Since the wheel turns 1 degree per second,
    . . in t seconds, radius OA has moved t degrees: . \angle AOB = t

    The height of the car is: h \:=\:AE \:=\:BD.

    In right triangle OBA\!:\;\;\cos t \:=\:\frac{OB}{10} \quad\Rightarrow\quad OB \:=\:10\cos t

    Then: . BD \:=\:OD - OB \:=\:15 - 10\cos t

    . . Therefore: . h \;=\;15 - 10\cos t

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  3. #3
    Junior Member
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    Thank you so much...I totally get this now. Thank you SO MUCH! You are amazing!
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