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Thread: Related rates of change

  1. #1 Related rates of change 
    Forum Ph.D. Heinsbergrelatz's Avatar
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    though i admit posting many questions up these days, its only because im trying to get rid of my doubts for my big exam coming up within few months time, so please understand :-D ;

    a man 1.5m tall is walking at a speed of away from a lamppost which has a lamp 5m above the ground.
    Find;
    a) the rate at which the length of his shadow is increasing
    b) the speed of the top of his shadow.


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  3. #2  
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    Can you provide your work up to this point so that there is evidence of your effort before providing the solution?


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  4. #3  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    to show that im not being fully lazy, i have gotten up to the point where you try and balance it out by using the pythagoras theorm, and then differentiating the , in a form of product rule, then i subsitute the in the product rule then i try look for the missing change rate of one side.... BUT then.. i dont know how to achieve the sides to use in the theorem.
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  5. #4  
    Forum Ph.D. Leszek Luchowski's Avatar
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    Think of two right triangles:

    Lamp bulb - tip of shadow - bottom of lamppost

    Lamp bulb - man's head - point on lamppost that's level with man's head.

    Use Thales' law; you don't even need Pythagoras.

    Good luck.
    Leszek. Pronounced [LEH-sheck]. The wondering Slav.
    History teaches us that we don't learn from history.
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  6. #5  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    thale's theorem? well yes i see that could be one way, thank you for the suggestion,
    but implicit differentiation also works right?
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  7. #6  
    Forum Ph.D. Leszek Luchowski's Avatar
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    Of course, as long as you don't break any rules of mathematics, you can get to your result in any way you wish.

    Personally, I don't see why you would insist on using much more complicated formuals than needed, but that's your choice.

    Good luck,
    L.
    Leszek. Pronounced [LEH-sheck]. The wondering Slav.
    History teaches us that we don't learn from history.
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  8. #7  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    thank you :-D
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