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Math Help - Rate of change - speed problem.

  1. #1
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    Unhappy Rate of change - speed problem.

    A ladder 5.1m long is placed on a 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?
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    Quote Originally Posted by bubbles73 View Post
    A ladder 5.1m long is placed on a 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?
    We have a right angled triangle, with sides x,y, and r.

    r is the hypotenuse, with a length of 5.1
    x is given as 2.4

    We solve for y and find it is 4.5

    x^2 + y^2 = r^2

    Differentiate.

    2x \frac{dx}{dt} + 2y \frac{dy}{dt} = 0 (Because r is a constant.)

    2(2.4)(1.5) + 2(4.5) \left( \frac{dy}{dt} \right) = 0

    Solve for \frac{dy}{dt}
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