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Math Help - Differentation

  1. #1
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    Question Differentation

    A ladder AB of length 5 metres has one end A leaning against a vertical wall. The other end B rests on horizontal ground. When A is at a height of 4 metres, it slides down the wall at a rate of 2 m/s. How fast is the other end, B, sliding along the horizontal ground? Answer: \frac{8}{3}m/s
    I'm confused by this question and do not know where to start. If I use the chain rule and write \frac{dB}{dt} = \frac{dB}{dx} \times \frac{dx}{dt} , where B is the length of the floor from the wall to point B and where t is the time, what would x be?
    I only know that when A is at a height of 4 metres, B must be at 3 metres away from the wall because of the pythagora's theorem.

    Any help would be appreciated and thank you in advance.
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  2. #2
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    Quote Originally Posted by caramelcake View Post
    I'm confused by this question and do not know where to start. If I use the chain rule and write \frac{dB}{dt} = \frac{dB}{dx} \times \frac{dx}{dt} , where B is the length of the floor from the wall to point B and where t is the time, what would x be?
    I only know that when A is at a height of 4 metres, B must be at 3 metres away from the wall because of the pythagora's theorem.

    Any help would be appreciated and thank you in advance.
    At time t, B^2 + x^2 = 5^2 ....
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    At time t, B^2 + x^2 = 5^2 ....
    What does x here represent?
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  4. #4
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    Quote Originally Posted by caramelcake View Post
    What does x here represent?
    B is the distance from the wall to the foot of the ladder

    5 is the length of the ladder

    x is the distance from the wall to the top of the ladder
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  5. #5
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    Quote Originally Posted by caramelcake View Post
    What does x here represent?
    The whole point of questions like this is that you introduce variables and set up the equation. Why have you written down an equation involving a pronumeral x when you don't know what x is!! (I had asumed you did not know an expression for x, but did know what x represented since it was your symbol in your equation).

    I think you need to go back to your class notes and textbook and review all the material and examples for related rates of change.
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