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math

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A ladder , 5 meter long , standing on a horizontal floor , leans against a vertical wall . If the top of the ladder slides downwards at the rate of 10 cm/sec . Find the rate at which the angle between the floor and the ladder is decreasing when the lower end of the ladder is 2 meter from the wall .

  • math - ,

    let the ladder reach h m high on the wall, let the base angle be Ø
    sinØ = h/5
    h = 5sinØ
    dh/dt = 5cosØ dØ/dt

    given: dh/dt = -10m/sec
    when base = 2m, cosØ = 2/5

    -10 = 5(2/5) dØ/dt
    dØ/dt = -5 radians/sec

    the angle is decreasing at a rate of 5 radians / sec

    (by using the word "decreasing" I do not include the negative sign)

  • math - ,

    Change first 5m to 500cm and 2m to 200cm and then solve using above procedure of reiny answer is 1/20 radians/sec

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