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Quadratic Functions Problem

  1. Sep 6, 2007 #1
    1. The problem statement, all variables and given/known data

    Suppose that an object is thrown into the air with an initial upward velocity of Vo meters per second from a height of ho meters above the ground.

    2. Relevant equations

    Then, t seconds later, its height (h(t) meters above the ground is modeled by the function h(t) = -4.9t^2 + Vot + ho.

    3. The attempt at a solution

    a) Find its height above the ground t seconds later.

    I got h(t) = -4.9t^2 + 14t + 30, and I checked the back of the book and it is correct.

    b) When will the stone reach its highest elevation?

    I tried a lot of things like plugging in various h's and t's, and using the quadratic formula, but I did not have much success.

    c) When will the stone hit the ground?

    Same as b), I wasn't sure where to start, but I made some educated guesses, however they proved wrong.

    NOTE: I have all of the correct answers. I am not asking for anyone to do my homework for me or give me the answers. I would just like to be guided in the right direction so I will never have to ask for help on these types of problems again. I have worked for 20 minutes straight on this problem, and I know for a fact it shouldn't take that long.

    Thank you for your time.
  2. jcsd
  3. Sep 6, 2007 #2


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    Homework Helper

    Well if [tex]h(t) = -4.9t^2 + 14t + 30[/tex] doesn't this represent a parabolic curve? doesnt this curve have a maximum point...which would correspond to the max height and the time it occurs
  4. Sep 6, 2007 #3

    How do you find the maximum value of the parabolic curve, though?
  5. Sep 6, 2007 #4


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    Homework Helper

    Find the the first derivative and equate to zero and solve for t
  6. Sep 6, 2007 #5
    Would you mind clarifying what you mean by "the first derivative?" I don't quite understand what you mean. Thanks.
  7. Sep 6, 2007 #6


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    Staff Emeritus
    Science Advisor

    You will meet the derivative in Calculus and can use it to solve more comples problems. Here, because this is a quadratic, you can find the vertex of the graph by completing the square. That will give you the highest point.
  8. Sep 6, 2007 #7
    Thanks for the assistance!
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