Calculus

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a 16 foot ladder is leaning against a building. the bottom of the ladder os sliding along the pavement at 3 ft/s How fast is the top of the ladder moving down when the foot of the ladder is 2 ft from the wall

  • Calculus -

    Let the distance of the bottom of the ladder from the wall be x, and let the distance of the top of the ladder from the floor be y.
    x^2 + y^2 = 256

    You want to know dy/dt when dx/dt = 3 and x = 2. At that time, y^2 = 252 and y = 15.87
    2x *dx/dt + 2y*dy/dt = 0

    dy/dt = -(x/y)*dx/dt = -0.126 dx/dt

    Use that equation to calculate dy/dt

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