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Thread: derivative function

  1. #1
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    Unhappy derivative function

    Q. A floodlight illumines a tall vertical wall that is 6 m from it. a man 2 m tall walks toward the wall in front of the light.
    a) find a function that gives the height of his shadow as a function of his distance from the light.
    Is this a formula I should know??
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by smckinlay View Post
    Q. A floodlight illumines a tall vertical wall that is 6 m from it. a man 2 m tall walks toward the wall in front of the light.
    a) find a function that gives the height of his shadow as a function of his distance from the light.
    Is this a formula I should know??
    No, but you should be able to construct it (this is the geometry part of the problem).

    CB
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  3. #3
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    I'm still lost. Assuming at 6 m the shadow is 2 m, and that as he approaches the wall the shadow increases - one point isn't enough to determine a function.
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  4. #4
    Super Member Failure's Avatar
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    Quote Originally Posted by smckinlay View Post
    I'm still lost. Assuming at 6 m the shadow is 2 m, and that as he approaches the wall the shadow increases - one point isn't enough to determine a function.
    First, make a drawing of the situation (see attached image).
    Let d be the distance of the man to the light (in meters) and $\displaystyle s(d)$ the height of his shadow on the wall (again in meters). By similarity of the right triangles with legs 2 and d, and legs s(d) and 6, respectively, in such a drawing you find that $\displaystyle s(d):6=2:d$, and, therefore, that $\displaystyle s(d)=12/d$.
    So if the man stands right next to the wall, i.e. $\displaystyle d=6$, we have $\displaystyle s(d)=2$, which seems reasonable enough.
    If the man is sufficiently close to the light, i.e. $\displaystyle d\approx 0$, we have that $\displaystyle s(d)\approx +\infty$, which may seem somewhat extreme but, if you think about it, isn't entirely unexpected either...
    Attached Thumbnails Attached Thumbnails derivative function-mathforum.png  
    Last edited by Failure; Aug 1st 2009 at 10:21 PM.
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