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Math Help - related rates: rolling wheel

  1. #1
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    related rates: rolling wheel

    A wheel with radius 2 m rolls at 18 rad/s. How fast is a point on the rim of the wheel rising when the point is pi
    /3 radians above the horizontal (and rising)? (Round your answer to one decimal

    place.)
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  2. #2
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    Lexington, MA (USA)
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    Hello, drewbear!

    A wheel with radius 2 m rolls at 18 rad/s.
    How fast is a point on the rim of the wheel rising when the point
    is \tfrac{\pi}{3} radians above the horizontal and rising?
    (Round your answer to one decimal place.)
    Code:
                  * * *
              *           *  P
            *               o
           *           2  *  *
                        *
          *           * θ     *
          *         o - - - - *
          *         C         *
    
           *                 *
            *               *
              *           *
                  * * *

    The parametric equations of point P are: . \begin{Bmatrix}x &=& 2\cos\theta & [1] \\ y &=& 2\sin\theta & [2] \end{Bmatrix}

    \text{We want }\,\frac{dy}{dt}\,\text{ when }\theta = \frac{\pi}{3}


    Differentiate [2] with respect to time: . \frac{dy}{dt} \;=\;2\cos\theta\,\frac{d\theta}{dt}


    We know that: . \cos\frac{\pi}{3} \,=\,\frac{1}{2},\;\;\frac{d\theta}{dt} \,=\,18

    Therefore: . \frac{dy}{dt} \;=\;2\left(\tfrac{1}{2}\right)(18) \;=\;18\text{ cm/sec}

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  3. #3
    Junior Member
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    thank you so much Soroban!!!
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