Long Related-Rates Problem. Please Help!

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Stpayne55

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(a) A Company is seeking to track aircraft that fly through its property. The company has two radar stations, one in city A and one in City B. B is one mile due east of A. For an aircraft each station can detect the aircraft's distance from the station and the rate at which this distance is changing. for any aircraft, 4 measurements are taken. The company wants to determine the location of a plane measured according to a specific grid. The origin is to be at the A station, one axis is to run due east (and west) of city A, and the other axis is to run due north (and south) of city A. the company also wants to determine an aircraft's velocity broken into its N,S,E, and West coordinates. Devise a means to recover the desired data from the measured data for the Company. Before the company president left, he mentioned that the company ran some sample flights with full data so that we can check how well the formulas they derive work. After some time, the data arrived. While the test plane was 5 miles due north of city B and flying due south at 100 miles per hour, the B station measured a distance of 5.022 miles and a rate of decrease of 99.555 miles per hour. The distance of the plane to the City A station was measured as 5.121 miles and was decreasing at 97.638 miles per hour. Later the test plane was five miles north and six miles east of A, and it was flying at 100 miles per hour in the direction 45 degrees south of east. At this time its distance to the A station was measured at 7.825 miles and was measured to be increasing at 9.037 miles per hour. The distance to the B station was 7.087 miles, and the rate of change of this distance was measured as zero miles per hour.


determine formulas that give the location and velocity of any plane. Then check them with their measured data. In addition, yo should comment on any assumptions that you had to make.The data carry one very serious limitation you should discover. I have no clue where to start! Any help?!?
 
Stpayne55 said:
(a) A Company is seeking to track aircraft that fly through its property. The company has two radar stations, one in city A and one in City B. B is one mile due east of A. For an aircraft each station can detect the aircraft's distance from the station and the rate at which this distance is changing. for any aircraft, 4 measurements are taken. The company wants to determine the location of a plane measured according to a specific grid. The origin is to be at the A station, one axis is to run due east (and west) of city A, and the other axis is to run due north (and south) of city A. the company also wants to determine an aircraft's velocity broken into its N,S,E, and West coordinates. Devise a means to recover the desired data from the measured data for the Company. Before the company president left, he mentioned that the company ran some sample flights with full data so that we can check how well the formulas they derive work. After some time, the data arrived. While the test plane was 5 miles due north of city B and flying due south at 100 miles per hour, the B station measured a distance of 5.022 miles and a rate of decrease of 99.555 miles per hour. The distance of the plane to the City A station was measured as 5.121 miles and was decreasing at 97.638 miles per hour. Later the test plane was five miles north and six miles east of A, and it was flying at 100 miles per hour in the direction 45 degrees south of east. At this time its distance to the A station was measured at 7.825 miles and was measured to be increasing at 9.037 miles per hour. The distance to the B station was 7.087 miles, and the rate of change of this distance was measured as zero miles per hour.


determine formulas that give the location and velocity of any plane. Then check them with their measured data. In addition, yo should comment on any assumptions that you had to make.The data carry one very serious limitation you should discover. I have no clue where to start! Any help?!?
Click to expand...

You can start first by reading this: READ BEFORE POSTING then I'd suggest at least drawing a picture and writing down the givens.
 
Sry, I'm a freshman in college. I've taken algebra and pre-calc within the last year and pre-calc was accelerated so my trig is weak at best I would say. We're learning derivatives currently and I don't know them well enough to apply them to this kind of problem. Any help?
 
Here is a link to what I have so far also. Sry, this forum won't let be directly add a photo from my iPad:

Airplane.JPG
 
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imagejpeg
Got the photo! Sry, this is really buggy on my ipad
 
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Oh sry, didn't realize you uploaded it. I thought it just grabbed it from that link. Thank you. Any ideas? Btw A and B are the radar stations. The point at the top of the triangle(unlabeled) is the airplane. I basically think I need to derive formulas to yield the given data. I believe I'm finding the derivatives of a, and x(base of triangle) with respect to A. Does this seem correct?
 
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