Calculus

posted by TraiShaun

A ladder 8 meters long is leaning against a wall. If the top of the ladder is slipping down at the rate of 8 meters per second, how fast is the bottom moving away from the wall when it is 7 meters from the wall?

Please give your answer in , enter it without the units.

  1. Steve

    When the ladder base is 7m from the wall, the top is √(64-49) = √15 from the ground.

    When the base is x meters from the wall,

    x^2 + h^2 = 64
    2x dx/dt + 2h dh/dt = 0
    2(7)dx/dt + 2√15 (-8) = 0

    dx/dt = 16√15/14 = 4.43m/s

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