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Math Help - Finding the restricted domain of a time/distance problem.

  1. #1
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    Finding the restricted domain of a time/distance problem.

    The question is: After a football is punted its height, h, in meters above the ground at t seconds can be modelled by h(t)=-4.9t^2+21t +0.45. Determine the restricted domain of this model.

    I was also asked to find the maximum height and what time it reached that height and had no difficulty.

    I have no idea at all how to find the restricted domain.
    Last edited by Apathy; January 12th 2011 at 04:28 PM.
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  2. #2
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    What are the t intercepts? (Time can't be negative)

    Max height: set the first derivative equal to 0 and solve for t.
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  3. #3
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    I've already solved the max height and solved the time it reached the height. The T intercept isn't indicated, is that what I am looking for to find the restricted domain? Should I do y=mx+b and find it?
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  4. #4
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    That formula doesn't apply until the ball is kicked (t= 0) and does not apply after the ball hits the ground, h(t)= 0. dwsmith said "t-intercepts" but I think he mean "h-intercepts", where h= 0. However, the ball is kicked from a height of .45 meters, not 0, so only the positive h-intercept is valid.
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    You need to find where the parabola crosses the t-axis.
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    the answer in the book is 0<t<or=4.3. The 0 is logical (although shouldn't I prove it somehow?) but I don't know where the 4.3 comes from.
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  7. #7
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    Quote Originally Posted by Apathy View Post
    the answer in the book is 0<t<or=4.3. The 0 is logical (although shouldn't I prove it somehow?) but I don't know where the 4.3 comes from.
    h(t)=-4.9t^2+21t +0.45=-4.9(t-4.307036...)(t+.02132248....)=0\Rightarrow t=-.021, \ 4.307

    Time starts at 0 so only one t value is valid.
    Last edited by dwsmith; January 12th 2011 at 04:28 PM. Reason: Added t.
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  8. #8
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    Quote Originally Posted by dwsmith View Post
    h(t)=-4.9^2+21t +0.45=-4.9(t-4.307036...)(t+.02132248....)=0\Rightarrow t=-.021, \ 4.307

    Time starts at 0 so only one t value is valid.
    Sorry It's actually h(t)=-4.9t^2+21t +0.45

    SO I should sub in 0... that would get me 2 answers and I just reject the one below 0. Does that sound good?
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    That was a typo. The factored form is still correct.
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  10. #10
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    Quote Originally Posted by Apathy View Post
    Sorry It's actually h(t)=-4.9t^2+21t +0.45

    SO I should sub in 0... that would get me 2 answers and I just reject the one below 0. Does that sound good?
    Sub 0 into where?

    Set h(t) = 0
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  11. #11
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    Wait you just factored out -4.9? That would still leave a t^2... the only way I could think of factoring it otherwise would be product/sum method but that would be very hard with decimals like this...
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  12. #12
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    Quote Originally Posted by Apathy View Post
    Wait you just factored out -4.9? That would still leave a t^2... the only way I could think of factoring it otherwise would be product/sum method but that would be very hard with decimals like this...
    You need to solve a quadratic equation. Have you been taught how to do so eg. using quadratic formula?
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