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Math Help - Curvlinear motion- ladder problem

  1. #1
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    Curvlinear motion- ladder problem

    A ladder is resting against a vertical wall.The top slides down in the -y direction and the bottom in the -x direction.
    What is dtheta/dt (where theta is the angle btw x axis and ladder)when the top of the ladder has -2.6m/s j and the angle btw the x axis and ladder is 26deg.

    I have worked out that the i component of vel is 0.634039m/s,but dont know how to calculate dtheta/dt.
    Length of ladder is 0.155meters

    ans=-18.663 rad/s
    Last edited by heatly; September 30th 2010 at 04:47 PM.
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  2. #2
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    This is a related rates problem. You need a general relationship between theta and y. After you get that, you can differentiate it (possibly using implicit differentiation) to get a relationship between dtheta/dt and dy/dt.
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    Quote Originally Posted by heatly View Post
    A ladder is resting against a vertical wall.The top slides down in the -y direction and the bottom in the -x direction.
    What is dtheta/dt (where theta is the angle btw x axis and ladder)when the top of the ladder has -2.6m/s j and the angle btw the x axis and ladder is 26deg.

    I have worked out that the i component of vel is 0.634039m/s,but dont know how to calculate dtheta/dt.
    Length of ladder is 0.155meters
    a ladder L = 0.155 \, m ... for a flea circus?

    \theta = \arctan\left(\frac{y}{x}\right)

    \displaystyle \frac{d\theta}{dt} = \frac{x \cdot \frac{dy}{dt} - y \cdot \frac{dx}{dt}}{x^2} \cdot \frac{x^2}{x^2+y^2} = \frac{x \cdot \frac{dy}{dt} - y \cdot \frac{dx}{dt}}{L^2}
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