Quadratic Functions Problem

  • Thread starter TbbZz
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  • #1
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Homework Statement



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.

Homework 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.

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.
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
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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
 
  • #3
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Yes.

How do you find the maximum value of the parabolic curve, though?
 
  • #4
rock.freak667
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Find the the first derivative and equate to zero and solve for t
 
  • #5
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Find the the first derivative and equate to zero and solve for t

Would you mind clarifying what you mean by "the first derivative?" I don't quite understand what you mean. Thanks.
 
  • #6
HallsofIvy
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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.
 
  • #7
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Thanks for the assistance!
 

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