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A ladder 25ft long is leaning against the wall of a house. The ladder is pulled away from the wall at a rate of 2 ft per second. How fast is the top of the ladder moving down the wall when its base is 7ft from the wall?

  • Calc. -

    This is the classic problem that almost every text in Calculus uses to introduce "rate of change"

    Make a diagram
    Let the ladder by y ft above the ground, and
    x ft away from the wall

    so you have a right angled triangle
    x^2 + y^2 = 25
    2x dx/dt + 2y dy/dt = 0 (#1)

    given : dx/dt = 2 ft/s
    find : dy/dt when x = 7

    when x = 7
    49 + y^2 = 625
    y = √576 = 24

    back in #1
    2(7)(2) + 2(24)dy/dt = 0
    dy/dt = -28/48 = -7/12 ft/s

    the negative indicates that the value of y is decreasing, or in other words, the ladder is dropping along the wall

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