math

A ladder 10 m long rests on horizontal ground and leans against a
vertical wall. The foot of the ladder is pulled away from the wall at 2
m/s. How fast is the top sliding down the wall when the foot of the
ladder is 6m from the wall?

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  1. x^2 + y^2 = 100 , where x is the base, y the height

    2x dx/dt + 2y dy/dt = 0

    given: dx/dt = 2 , and x = 6
    then 36+y^2 = 100
    y^2 = 64
    y = 8

    in
    2x dx/dt + 2y dy/dt = 0
    2(6)(2) + 2(8)dy/dt = 0
    dy/dt = -24/16 = -3/2

    it is sliding down at 3/2 m/sec

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  2. Let x represent the length of the ladder =10meters+5meters=x =x=10m+5m =15m :the length of the ladder is 10m

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