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Math Help - Background Infor on This Problem

  1. #1
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    Background Infor on This Problem

    http://www.stewartcalculus.com/data/...p_0205_stu.pdf

    Im not looking for an answer to this problem (not trying to have others do my work for me). However, I could use a little help in understanding the background information for this problem. Specifically, what particular laws or equations come into play here? What theorems and background information should I brush up in order to get started? Understanding specifically what is being asked in a word problem has always been my weak point. Thanks in advance.
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  2. #2
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    Looks like you need to know how to calculate the derivative, how to model with polynomials, and the relationship between derivative and acceleration. More specifically, you need to know what it would mean for the function P(x) to represent height h at distance l, and height 0 at distance 0. You should also use the hint about putting a restriction on P'(x). There's a nice property that you want the graph to have near the origin and at the start of descent. Looks like you'll need to solve a system of equations at some point, too.
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  3. #3
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    Thanks for the info. I was able to get most of the problem alright after that (we are allowed to submit two drafts of our work for professor review prior to the final being handed in) but am stumbling on the last point which, ironically enough, seems the easiest. Here is how I arrived at my answer:

    If an airplane is not allowed to exceed 860 miles/h^2 and the cruising altitude is 35,000 feet and the speed is 300 miles/h Given the formula (6hv^2)/l^2 is less than or equal to k Find how far away the pilot should start the descent. Here is how I calculated:

    h = 35,000 feet X (1 mile/5280 feet) = 6.63 miles
    v = 300 miles/h
    l = unknown
    k = 860 miles/hour

    (6hv^2)/l^2 = k
    l^2 = (6hv^2)/k
    l^2 = [(6)(6.63)(300^2)]/860
    l^2 = 4163.02
    l = 64.52

    My professor says this number is too large but all my math seems right. Any idea where I screwed up?
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