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Thread: Related Rates Help

  1. #1

    Question Related Rates Help

    A street light is mounted at the top of a 15 foot pole. A man 6 feet tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of his shadow moving when he is 40 feet from the pole?

    What would be the process used to solve this problem and related rates in general? I dont necessarily care about the answer more the solution, showing how to solve these kinds of problems. Thanks!

  2. #2
    Elite Member stapel's Avatar
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    Quote Originally Posted by maumpowj View Post
    A street light is mounted at the top of a 15 foot pole. A man 6 feet tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of his shadow moving when he is 40 feet from the pole?

    What would be the process used to solve this problem and related rates in general? I dont necessarily care about the answer more the solution, showing how to solve these kinds of problems. Thanks!
    A good start would be to draw a schematic of the situation. Draw a right triangle with two "height" lines:

    Code:
    * .
    |    ' .
    |15  |    ' .
    |    |6        ' .
    *----*-------------*
    |  x |     y       |
    From the exercise, you know that dx/dt = 5, and you are needing to find dy/dt when x = 40. Can you think of a way to approach this?

  3. #3
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    Quote Originally Posted by stapel View Post
    A good start would be to draw a schematic of the situation. Draw a right triangle with two "height" lines:

    Code:
    * .
    |    ' .
    |15  |    ' .
    |    |6        ' .
    *----*-------------*
    |  x |     y       |
    From the exercise, you know that dx/dt = 5, and you are needing to find dy/dt when x = 40. Can you think of a way to approach this?
    Technically, dy/dt is the rate the shadow moves. d(x + y)/dt is the rate the tip of the shadow moves which is simply the sum of dx/dt and dy/dt.
    "There are 10 types of people in this world - those who understand binary and those who don't."

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