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Math Help - Relative Rate Problem

  1. #1
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    Relative Rate Problem

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

    Apparently, I've been doing too many calculus problems of late because I read this as they are saying that a dude is walking at 5 ft/second and are asking me how fast his shadow is moving. How can this answer be anything other than 5 ft/s? They are obviously asking for dx/dt, but they give us dx/dt!!!

    Can somebody set me straight so that I can tackle this problem. I am clearly missing something.

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

    Apparently, I've been doing too many calculus problems of late because I read this as they are saying that a dude is walking at 5 ft/second and are asking me how fast his shadow is moving. How can this answer be anything other than 5 ft/s? They are obviously asking for dx/dt, but they give us dx/dt!!!

    Can somebody set me straight so that I can tackle this problem. I am clearly missing something.

    Thanks.
    the shadow has two ends... one is at the foot of the dude and the other is found out by using similarity. in the quaestion the velocity of the other tip with respect to ground( pole in this case) is being asked.
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  3. #3
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    I got it figured out. There two things happening to the shadow. One is that it is moving at 5 ft/second. The other is that it is growing in length. This wasn't apparent to me at first. Thanks.
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