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A ladder 10 meter long is leaning against a wall. If the top of the ladder is sliding down the wall at 3m/s, how fast is the angle between the top of the ladder and the wall changing when the foot of the ladder is 6 meter away from the wall?

  • mathematic -

    let the angle you mentioned be Ø
    Let the foot of the ladder be x ft from the wall, and the height of the ladder be y ft
    cosØ = y/10
    y = 10cosØ
    dy/dt = -10sinØ dØ/dt

    when x = 6
    x^2+y^2=100
    y = 8 , and sinØ = 8/10
    Also we know dy/dt = -3 m/s

    -3 = -10(8/10)(dØ/dt)
    dØ/dt = 3/8 radians/s

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