a street light is mounted at the top of a 15 foot pole. A man 6 ft tall walks away from the pole wit a speed of 7 ft/s along a straight path

Question

a street light is mounted at the top of a 15 foot pole. A man 6 ft tall walks away from the pole wit a speed of 7 ft/s along a straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole

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Mộc Miên 6 months 2021-08-27T20:25:18+00:00 1 Answers 0 views 0

Answers ( )

  1. quangkhai
    0
    2021-08-27T20:27:09+00:00
    Reply

    Answer:

    16.3 ft/s

    Explanation:

    Let d=distance

    and

    x = length of shadow.

    Therfore,

    x=(d + x)

     = 6/15

    So,

        15x = 6x + 6d

         9x = 6d.

    x = (2/3)d.

    As we know that:

    dx=dt

       = (2/3) (d/dt) 

    Also,

    Given:

    d(d)=dt

         = 7 ft/s

    Thus,

    d(d + x)=dt

               = (7/3)d (d/dt)

    Substitute, d= 7  

    d(d + x) = 49/3 ft/s.

    Hence,

    d(d + x) = 16.3 ft/s.

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