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Math Help - differential story problem

  1. #1
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    differential story problem

    here's the problem;

    "Suppose an observer is on top of a skyscraper that is 1000 ft. If a car is moving away from the base of the skyscraper at a constant speed of 40 ft/sec, how fast is the distance from the observer to the car increasing when the car is 500 ft from the skyscraper?"

    so far, i have the equation a^2 = 1000^2 + c^2 which i was going to differentiate but i dont know if thats right. please someone help me to do this..
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  2. #2
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    Quote Originally Posted by Arez View Post
    here's the problem;

    "Suppose an observer is on top of a skyscraper that is 1000 ft. If a car is moving away from the base of the skyscraper at a constant speed of 40 ft/sec, how fast is the distance from the observer to the car increasing when the car is 500 ft from the skyscraper?"

    so far, i have the equation a^2 = 1000^2 + c^2 which i was going to differentiate but i dont know if thats right. please someone help me to do this..
    if a = car/observer distance
    c = car/building base distance,
    then your equation is fine.

    find \frac{da}{dt} when c = 500
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  3. #3
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    Quote Originally Posted by Arez View Post
    here's the problem;

    "Suppose an observer is on top of a skyscraper that is 1000 ft. If a car is moving away from the base of the skyscraper at a constant speed of 40 ft/sec, how fast is the distance from the observer to the car increasing when the car is 500 ft from the skyscraper?"

    so far, i have the equation a^2 = 1000^2 + c^2 which i was going to differentiate but i dont know if thats right. please someone help me to do this..
    No one can tell you if that is right because you have not said what "a" and "c" represent! Always do that at the beginning of a problem:
    "a is the straight line distance from the top of the skyscraper and c is the distance from the base of the skyscraper to the car."
    Once you have said that then you can use the Pythagorean theorem to say that a^2= 1000^2+ c^2. Yes, differentiate both sides of that and remember that you know dc/dt and are trying to find da/dt.
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