A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Calculus Rates & speed question about airplanes
anonymous
 one year ago
Calculus Rates & speed question about airplanes

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know the answer of a; how do I find the equation for the distance between the planes at all times for part b?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0its easier to read when its not in the chinese mode ...

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0its solveble, buti have to read thru it first, and these old eyes get tired at times

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0both at 33000 ft they intersect directly over Frada hgts near misses shortly after 130pm  at 130, Am2003 was 32 Nm from Frada, heading 171o at a rate of 405knots at 130 Un366 was 44 Nm from Frada, heading 81o at a rate of 465 knots

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0how how do we read airplane headings? from the north line right?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0doesnt really matter, the orientation is the same regardless of our 'proper' placements

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0lets draw a picture, both planes, and Frada

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohh ok I just assumed it was a right triangle and so drew a right triangle with 81 9 and 90

amistre64
 one year ago
Best ResponseYou've already chosen the best response.017181 = 90, so your assumption was valid

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we have that, we got the rate of the distance decreasing between them two, but we need to find the actual distance separation at the closest point. that is the part we are having trouble with

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433270115412:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the rate we got is 472.8 knots

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yup we have that already

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0d^2 = x^2 + y^2 rate of change is derivatives, so what is our derivative?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0jut making sure we are on the same page here

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0the shortest distance between them is when one of them is at Frada ... that is when they are in line with each other.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0what is our derivative? lets make sure we are working it thru and have not developed any errors

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hmm..how did you draw the triangle?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we got part a already, we got ds/dt = 494.7

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yyup thanks we already have that part; we got ds/dt = 497.7 already. we are only stuck on part b  thank you so much!

perl
 one year ago
Best ResponseYou've already chosen the best response.0for part b) i set AA = 32405t distance from Frada UA = 44 465t distance from frada Distance between AA and UA D= sqrt((32405*t)^2+(44465*t)^2) minimize this by taking the derivative dD/dt = (1/2)*(66840+760500*t)/sqrt((32405*t)^2+(44465*t)^2) set dD/dt = 0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that makes sense! we got t = .0879

perl
 one year ago
Best ResponseYou've already chosen the best response.0@amistre64 please check for part a) i got a different ds/dt x^2 + y^2 = s^2 2x x' + 2y y' = 2s s' x* x' + y* y' = s * s ' 44 * (465) + 32 * (405) = sqrt( 44^2 + 32^2 ) * s ' s' = [44 * (465) + 32 * (405)]/ sqrt( 44^2 + 32^2 ) s' = 614.27 knots

perl
 one year ago
Best ResponseYou've already chosen the best response.0right, t = 1114/12675 = .0878 is the time when their distance is closest. and if you plug in you get D = 4.7677 miles .

perl
 one year ago
Best ResponseYou've already chosen the best response.0do you agree with my work, how i got ds/dt = 614.27

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh!! we screwed it up thank you!!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.044 * (465) + 32 * (405) I think you had an error here...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think the speed of American 1003 is 405 not 465

perl
 one year ago
Best ResponseYou've already chosen the best response.0we can think of this problem as two dots approaching each other. The path of the dots can be represented by parametric equations

perl
 one year ago
Best ResponseYou've already chosen the best response.0woops i need a negative sign there

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do you know "whether ATC would have time to take action? Might a slight altitude change for one of the lights help prevent any five mile rule violation?"

perl
 one year ago
Best ResponseYou've already chosen the best response.0+465 since it is moving to the right

perl
 one year ago
Best ResponseYou've already chosen the best response.0now if you plug in t= .08 into both equations you can see exactly where the points are

perl
 one year ago
Best ResponseYou've already chosen the best response.0clearly AA gets to Frada before UA because 32405t = 0 , t= 32/405 ~ .079 sec 44 + 465t = 0, t= 44/464 ~ .094 sec but at t = 1114/12675 they are closest together plug in this time into AA and UA AA is below F by 3.59 nautical miles UA is to the left of Frada by 3.13 nautical miles

perl
 one year ago
Best ResponseYou've already chosen the best response.0if you change the altitude that could change the minimum 5 nautical miles rule. but we would have to go into three dimensions

perl
 one year ago
Best ResponseYou've already chosen the best response.0without loss of generality we can set one of the planes to 30,000 feet and the other one to some value A. But note that we must change units to nautical miles to be consistent with our earlier calculations.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.