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Calculus 1

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A ladder 10ft long rests against a vertical wall. If the bottom on the ladder slides away from the wall at 2 ft/s, how fast is the angle ladder makes with the ground changing when the bottom of the ladder is 5 ft from the wall.

  • Calculus 1 -

    Let the foot be x ft from the wall, let the angle formed by the ladder at the ground be Ø

    given: dx/dt = 2 ft/s
    find: dØ/dt when x = 5

    x/10 = cosØ
    x = 10cosØ
    dx/dt = -10sinØ dØ/dt

    when x=5,
    height^2 + 5^2 = 10^2
    height = √75

    2 = -10(√75/10) dØ/dt
    dØ/dt = - 2/√75 radians/second
    = appr. - .23 rad/s

  • Calculus 1 -

    100mph

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