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March 24, 2017

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a ladder is 20 feet long and its top is slidding at a constant rate of 2 feet per second. How fast is the bottom of the ladder moving along the ground when the bottom is 16 feet from the wall?

  • Calculus - ,

    Let the ladder be x ft from the wall, and y ft up along the wall
    x^2 + y^2 = 20^2
    2x dx/dt + 2y dy/dt = 0
    x dx/dt + y dy/dt = 0
    when x=16 , y^2 = 400-256 ---> y = 12
    and dy/dt = -2 ft/sec

    16(dx/dt) + 12(-2) = 0
    dx/dt = -24/16 = -3/2

    the ladder is moving away from the wall at 1.5 ft/s

  • Calculus - ,

    last two lines should have been

    16(dx/dt) + 12(-2) = 0
    dx/dt = 24/16 = 3/2

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