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Math Help - rectilinear motion/arc length

  1. #1
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    rectilinear motion/arc length

    I know the title is vague, but I'm not sure what this question is asking:

    A toy rocket is launched from the top of the building, it's height above the ground after t seconds is given by h(t)=-4.9t^2+19.6t+58.8. Find the total distance traveled from launch to crash.

    How would I go about finding that?
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  2. #2
    Super Member Quacky's Avatar
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    Look at this graph; it marks the path of the rocket.

    http://www.wolframalpha.com/input/?i=Plot+-4.9x^2%2B19.6x%2B58.8

    When will the crash occur? And how would you have proven this without using the graph? And can you find the distance?
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  3. #3
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    Quote Originally Posted by Quacky View Post
    Look at this graph; it marks the path of the rocket.

    http://www.wolframalpha.com/input/?i=Plot+-4.9x^2%2B19.6x%2B58.8

    When will the crash occur? And how would you have proven this without using the graph?
    h(6)=0?

    Edit: I'm not sure how I would find the distance.
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  4. #4
    Super Member Quacky's Avatar
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    That's right, but I realise that I'd misread your question.

    If it's the distance that you're looking for, then you need to find how high up the rocket travelled (this can be read off of the graph, but it's obviously far better to use calculus to find the maximum of the graph, and then subtract the initial height), then you need to find the distance down it travelled (this is just the height of the maximum) and add those together.

    Using the graph is inferior to calculus, but it does illustrate the problem. Have an attempt using calculus and see how you go.
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  5. #5
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    Quote Originally Posted by Quacky View Post
    That's right, but I realise that I'd misread your question.

    If it's the distance that you're looking for, then you need to find how high up the rocket travelled (this can be read off of the graph, but it's obviously far better to use calculus to find the maximum of the graph, and then subtract the initial height), then you need to find the distance down it travelled (this is just the height of the maximum) and add those together.

    Using the graph is inferior to calculus, but it does illustrate the problem. Have an attempt using calculus and see how you go.
    The max height is 78.4m, so I'm assuming it's (78.4-58.8)+78.4? Hopefully I understood that correctly. Thanks a lot for your help!
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  6. #6
    MHF Contributor Also sprach Zarathustra's Avatar
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  7. #7
    Super Member Quacky's Avatar
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    That's right, but I was assuming the question merely wanted the vertical distance travelled. Is this the case? If not, you'll have to use ASZ's method.
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