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Math Help - related rates

  1. #1
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    related rates

    i'm lost on the related rates chapter in calculus...so if anybody can please help me.

    A man 6 ft tall walks at the rate of 5 ft/ sectoward a streetlight that is 16 ft above the ground. At what rate is the length of his shadow changing when he is 10 ft from the base of the light?
    Last edited by turtle; October 29th 2006 at 06:12 PM.
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  2. #2
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    Did you leave out details about the light? And are the "particle" and the "man" the same thing?
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    oops, sorry......i mixed two different problems........
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    Quote Originally Posted by turtle View Post
    i'm lost on the related rates chapter in calculus...so if anybody can please help me.

    A man 6 ft tall walks at the rate of 5 ft/ sectoward a streetlight that is 16 ft above the ground. At what rate is the length of his shadow changing when he is 10 ft from the base of the light?
    x'(t)=-5ft/s
    Draw a right triangle base s+x, height 16 where s is the length of the shadow and x is the distance from the light.

    You can see that (s+x)/16=s/6
    Solve for x to get x=5s/3
    Implicitly differentiate both sides x'=5s'/3
    Solve for s'(t)=3x'(t)/5
    Plug x'(t)=-5 to get s'(t)=-3ft/s

    (I think this is right but I haven't done this in a few years so this is my disclaimer. Wait for someone to confirm if you want to be sure.)
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  5. #5
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    Quote Originally Posted by splash View Post
    x'(t)=-5ft/s
    Draw a right triangle base s+x, height 16 where s is the length of the shadow and x is the distance from the light.

    You can see that (s+x)/16=s/6
    Solve for x to get x=5s/3
    Implicitly differentiate both sides x'=5s'/3
    Solve for s'(t)=3x'(t)/5
    Plug x'(t)=-5 to get s'(t)=-3ft/s

    (I think this is right but I haven't done this in a few years so this is my disclaimer. Wait for someone to confirm if you want to be sure.)
    Looks good to me!

    -Dan
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