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Math Help - Shadows

  1. #1
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    Question Shadows

    A floodlight that is 15 m away and at ground level illuminates a building. A man 2 m tall walks away from the light directly towards the building at 2 m/s. Find the rate of change of the length of his shadow when he is 4 m from the light.

    so far i have the the ratio is that the shadow is 15/2 when he is 4 m away. but when i plug in to get the rate of change im way off...

    With the similar triangle do i have to compare the shadow to the length they give me or to his height???
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  2. #2
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    Quote Originally Posted by Tascja View Post
    A floodlight that is 15 m away and at ground level illuminates a building. A man 2 m tall walks away from the light directly towards the building at 2 m/s. Find the rate of change of the length of his shadow when he is 4 m from the light.

    so far i have the the ratio is that the shadow is 15/2 when he is 4 m away. but when i plug in to get the rate of change im way off...

    With the similar triangle do i have to compare the shadow to the length they give me or to his height???
    Hello Tascja,

    I've attached a sketch of the situation.

    t: elapsed time
    2*t: length of the way the man has walked in t seconds.

    The length of the shadow can be calculated:

    \frac{S}{15}=\frac{2}{4+2\cdot t}. Solve for S:

    S=\frac{30}{4+2\cdot t}=\frac{15}{2+ t}

    The first derivative of S will give the rate of change:

    S'(t)=-\frac{15}{(2+t)^2}

    EB
    Attached Thumbnails Attached Thumbnails Shadows-licht_schatten1.gif  
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