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Math Help - Project - I need some serious help.

  1. #1
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    Exclamation Project - I need some serious help.

    Alright, so I have a project due for Calculus - Like immediately and I need some help.

    here is what the project says (i've only included the important parts):

    We have been asked to investigate two flights, American Airlines flight #1003 (Minneapolis to New Orleans) and United Airlines flight #366 (Los Angeles to New York). Both flights are at 33,000 feet, and the flight paths intersect directly over our client's city of Frada Heights. A committee of concerned citizens has petitioned the City to investigate the possible danger of a collision of these two flights, based on the testimony of several residents who claim to have seen near-misses shortly after 1:30 PM on several occasions recently.


    On the day we checked, we found that at 1:30 PM (Central time), American 1003 was 32 nautical miles from Frada Heights, approaching it on a heading of 171 at a rate of 405 knots. At the same time, United 366 was 44 nautical miles from Frada Heights and was approaching it on a heading of 81 at a rate of 465 knots.


    The DPS has asked us to determine how fast the planes were approaching each other (i.e., how fast the distance between them was decreasing) at that time, hoping that we will testify that this approach was dangerously fast. The DPS would also like to know whether the flights would have violated the FAA's minimum separation requirement of 5 nautical miles. If possible, we would like to determine how close the planes actually get to each other, and the time at which they are closest. Would Air Traffic Control have time to take appropriate action? Might a slight altitude change for one of the flights help prevent any five mile rule violation?



    Some information that I have so far:



    hopefully this is right.

    1 Knot = 1 Nautical Mile per hour
    1 nautical mile per hour = 1 mile per hour
    1 nautical mile = 1852 meters

    So far i've gotten a map and traced where the planes are going. Frada Heights isn't a real place obviously but its suppose to be somewhere in Northern Missouri, this at least is where they intersect.

    Both planes are flying at the same altitude. I've made a triangle with the map i have - the triangle goes from where frada heights should be, over to NY and up to MN - if i'm correct if the lines on the triangle going down are proportional the planes are going to collide no matter what.

    My problem is I'm having trouble finding out how to actually get to my answers - is there an equation for relative velocity? Thats, i think, what i need to find between the two planes...

    Anyway - I would greatly appreciate anyones help on this. I'm new to the forums.

    Thanks in advance,

    -ty
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  2. #2
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    Quote Originally Posted by Tiger242008 View Post
    Alright, so I have a project due for Calculus - Like immediately and I need some help.
    [snip]
    -ty
    My very first thought was "I wonder when this project was given" .....

    Quote Originally Posted by Tiger242008 View Post
    [snip] is there an equation for relative velocity? [snip]
    Yes there is. Google those two magic words and see for yourself.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    My very first thought was "I wonder when this project was given" .....


    Yes there is. Google those two magic words and see for yourself.
    I asked my teacher exactly: Is relative velocity and average velocity the same thing, he tells me no - so far the only way I guessed how to find it, other than googling it yet, is finding the miles over which the planes have to cover, and divide/multiply that by how fast they're going in miles per hour. :/

    Which I still don't really understand what i'm getting at or what that is going to give me.
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  4. #4
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    velocity = \frac {change in distance}{change in time}
    The distance we are interested in is the distance between the two planes. So what you need to do is find the distance between the planes at any 2 times during their flights. Then apply the formula above.

    You could also do this question by subtracting one of the planes velocity vectors from the other and finding the absolute value. This is a far more computationally simple way of doing the problem, but I am not sure I could explain clearly why it works. A google search will undoubtedly reveal ssome sites that explain this more clearly than I could.
    Last edited by badgerigar; December 17th 2007 at 09:21 PM. Reason: Forgot math tags
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  5. #5
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    Sounds awesome badgerigar, I'll look into that, Thanks for all your help!

    If anyone else wants to post more please feel free to, I'm still looking at the problem many different ways.
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