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Math Help - Parabola Word Problem

  1. #1
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    Parabola Word Problem

    Mary is playing golf. The diagram below describes her situation. Determine the equation of this relation. Then find the time when the ball is 20m away from the hole.

    What I did so far was the following:

    Find a using P(0, 15) and s = -50, t = 50 into y=a(x-s)(x-t).

    15 = a(0-(-50))(0-50)
    15 = a(50)(-50)
    15 = 2500a
    3/500 = a

    Therefore the equation of this relation is y = 3/500(x+50)(x-50)

    Now the problem is, I'm not sure how to find the time. Do I substitute 20m into the above equation? Also, what units would the time be in?
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by shadow6 View Post
    Mary is playing golf. The diagram below describes her situation. Determine the equation of this relation. Then find the time when the ball is 20m away from the hole.

    What I did so far was the following:

    Find a using P(0, 15) and s = -50, t = 50 into y=a(x-s)(x-t).

    15 = a(0-(-50))(0-50)
    15 = a(50)(-50)
    15 = 2500a
    3/500 = a

    Therefore the equation of this relation is y = 3/500(x+50)(x-50)

    Now the problem is, I'm not sure how to find the time. Do I substitute 20m into the above equation? Also, what units would the time be in?
    20 meters from the hole means that it is 30 meters from the origin. so you plug in either x=30 or x=-30, depending on which end the hole is. but the answer should be the same here (the y-coordinates are equal at x=30 and x=-30).

    Good luck!!
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  3. #3
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    EDIT: apcalculus answered my question.


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