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Math Help - 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 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 s(d):6=2:d, and, therefore, that s(d)=12/d.
    So if the man stands right next to the wall, i.e. d=6, we have s(d)=2, which seems reasonable enough.
    If the man is sufficiently close to the light, i.e. d\approx 0, we have that 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; August 1st 2009 at 10:21 PM.
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