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Math Help - Rates of change question

  1. #1
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    Rates of change question

    Hello

    I have a maths exam tomorrow, this is one question I cannot get

    Any help is GREATLY appreciated!!!

    A ladder 5.1m long is pushed on level ground against a vertical wall. The foot of the ladder is pushed towards the wall at 1.5m/s. At what rate is the top of the ladder rising when its bottom is 2.4m from the wall?

    Thanks a lot!!

    Lachlan
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  2. #2
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    Quote Originally Posted by auonline View Post
    Hello

    I have a maths exam tomorrow, this is one question I cannot get

    Any help is GREATLY appreciated!!!

    A ladder 5.1m long is pushed on level ground against a vertical wall. The foot of the ladder is pushed towards the wall at 1.5m/s. At what rate is the top of the ladder rising when its bottom is 2.4m from the wall?

    Thanks a lot!!

    Lachlan
    First draw a picture. You should see a right triangle with the ladder, of length 5.1 m, as hypotenuse. If you use x and y to me the "base" and "height" of that triangle, x^2+ y^2= (5.1)^2. Change that "static" equation into a "dynamic" equation by differentiating each side with respect to x: 2x\frac{dx}{dt}+ 2y\frac{dy}{dt}= 0. You are told that x= 2.4 and \frac{dx}{dt}= -1.5. You can solve (2.4)^2+ y^2= (5.1)^2 for y and then solve 2(2.4)(-1.4)+ 2y\frac{dy}{dt}= 0 for \frac{dy}{dt}.
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  3. #3
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    I can't believe I didn't think of doing that!!

    + rep and thank'd.

    Thanks

    Lachlan =D
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