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Thread: Shadows and distance, I need a formula to solve for Object 2

  1. Mar 20th 2012, 06:25 AM #1
    crah28
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    Shadows and distance, I need a formula to solve for Object 2

    Looking for a formula to solve this word problem. Please Help

    A shadow from object 1 projects on a wall 1.75 X larger than its original size. Object 1 is 4.5 ft from the wall the shadow has been casted on. Object 2 has a known size which cast a shadow of 1.25 X its original size. How far is object 2 from the wall.
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  2. Mar 20th 2012, 09:39 PM #2
    princeps
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    Re: Shadows and distance, I need a formula to solve for Object 2

    Quote Originally Posted by crah28 View Post
    Looking for a formula to solve this word problem. Please Help

    A shadow from object 1 projects on a wall 1.75 X larger than its original size. Object 1 is 4.5 ft from the wall the shadow has been casted on. Object 2 has a known size which cast a shadow of 1.25 X its original size. How far is object 2 from the wall.
    Let :

    r_1=1.75~ , r_2=1.25~ ,x_1=4.5 ~ , x_2 = ?

    and denote distance of the source of the light from the wall as d . Therefore :

    d=r_1(d-x_1) \Rightarrow d=1.75(d-4.5) \Rightarrow d=10.5

    Hence :

    d=r_2(d-x_2) \Rightarrow x_2=\frac{dr_2-d}{r_2} \Rightarrow x_2=2.1
    Thanks from crah28
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  3. Mar 21st 2012, 07:20 AM #3
    crah28
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    Thumbs up Re: Shadows and distance, I need a formula to solve for Object 2

    Thanks for your help, the formula was spot on.
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