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Math Help - Help solve this related rate problem

  1. #1
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    Unhappy Help solve this related rate problem

    A conical pendulum consists of a mass m, attached to a string of fixed length L, that travels around a circle of radius r at a fixed velocity v. As the velocity of the mass is increased, both the radius and angle x increase. Given that v^2 = r*g*tan(x), where g is a gravitational constant, find the relationship between the related rates

    a) dv/dt and dx/dt
    b) dv/dt and dr/dt
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  2. #2
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    Quote Originally Posted by zEr0ne View Post
    A conical pendulum consists of a mass m, attached to a string of fixed length L, that travels around a circle of radius r at a fixed velocity v. As the velocity of the mass is increased, both the radius and angle x increase. Given that v^2 = r*g*tan(x), where g is a gravitational constant, find the relationship between the related rates

    a) dv/dt and dx/dt
    b) dv/dt and dr/dt
    \frac{d}{dt}[v^2 = rg\tan{x}]

    2v \cdot \frac{dv}{dt} = g\left[r \cdot \sec^2{x} \cdot \frac{dx}{dt} + \tan{x} \cdot \frac{dr}{dt}\right]


    note that r = L\sin{x}

    so ...

    \frac{dr}{dt} = L\cos{x} \cdot \frac{dx}{dt}

    and

    \frac{dx}{dt} = \frac{\sec{x}}{L} \cdot \frac{dr}{dt}

    given the above relationships, you should be able to finish up and answer the questions.
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