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anonymous

  • one year ago

I need help with this problem!! It would be much appreciated!! A street light is mounted at the top of a 15 foot-tall pole. A man 6ft tall walks away from the pole with the speed of 5ft/s along a straight path. How fast is the tip of his shadow moving away from the pole when he is 40ft from the pole?

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  1. ganeshie8
    • one year ago
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    |dw:1434097565386:dw|

  2. anonymous
    • one year ago
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    Right, and I think we have to use similar triangles, correct?

  3. ganeshie8
    • one year ago
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    Yes! lets start by labelling stuff

  4. ganeshie8
    • one year ago
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    Say the lamppost is the origin, \(\large y\) represents the position of shadow, \(\large x\) represents the position of man |dw:1434098052886:dw|

  5. ganeshie8
    • one year ago
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    we're given \( \dfrac{dx}{dt}=5 \) and asked to find \(\dfrac{dy}{dt}\)

  6. anonymous
    • one year ago
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    Exactly! I got stuck right here, I don't know what to do from here on

  7. ganeshie8
    • one year ago
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    do you see two similar triangles ?

  8. anonymous
    • one year ago
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    Yeah, one with 15 and y, the other with 6 and y-x

  9. ganeshie8
    • one year ago
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    |dw:1434098406881:dw|

  10. ganeshie8
    • one year ago
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    set up a proportion: \[\large \dfrac{15}{y}~~=~~\dfrac{6}{y-x}\]

  11. ganeshie8
    • one year ago
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    rearrange a bit and differentiate with respect to \(t\)

  12. anonymous
    • one year ago
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    Ohhh okay! Im gonna do that and tell you what i get

  13. anonymous
    • one year ago
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    So is dy/dt = (15(5))/9 ??

  14. ganeshie8
    • one year ago
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    Yes, looks you can cancel 3 and simplify a bit more

  15. anonymous
    • one year ago
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    Great!! Thanks so much!! You saved me! :D

  16. ganeshie8
    • one year ago
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    np:)

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