Results 1 to 2 of 2

Math Help - Related Rates

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    229

    Related Rates

    An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each other. One airplane is 150 miles from the point and has a speed of 450 miles per hour. The other is 200 miles from the point and has a speed of 600 miles per hour.

    At what rate is the distance between the planes changing?

    - I'm completely lost on this question. I don't know how to proceed.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,035
    Thanks
    49
    One way is to notice we have all the bits for Pythagoras...



    So differentiate implicitly, using...



    ... the chain rule, where straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case time), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

    Spoiler:


    Then sub in the distances and speeds.


    __________________________________________

    Don't integrate - balloontegrate!

    Balloon Calculus: Gallery

    Balloon Calculus Drawing with LaTeX and Asymptote!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Related Rates
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 26th 2009, 08:54 PM
  2. Rates and Related Rates!!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 2nd 2008, 10:53 AM
  3. Another Related Rates
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 13th 2008, 06:32 AM
  4. Related Rates
    Posted in the Calculus Forum
    Replies: 6
    Last Post: March 12th 2008, 05:49 PM
  5. rates and related rates
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 29th 2007, 09:51 PM

Search Tags


/mathhelpforum @mathhelpforum