Results 1 to 3 of 3

Math Help - Implicit differentiation applications (exam tomorrow!)

  1. #1
    Super Member
    Joined
    Mar 2006
    Posts
    705
    Thanks
    2

    Implicit differentiation applications (exam tomorrow!)

    Q: A plane flying with a constant speed of 24 km/min passes over a ground radar station at an altitude of 4 km and climbs at an angle of 30 degrees. At what rate, in km/min is the distance from the plane to the radar station increasing 3 minutes later?

    A: I let the trangle sides be A, B, and C; A is the initial distance between
    radar and the plane (4km); B is the distance between initial position of
    the plane to 3 mins later (24km x 3min = 72); C is the final distance between radar to plane.

    so I have C^2 = 4^2 + 72^2 - (2)(4)(72)cos(120 degrees)

    Solved for C = 5488km, but the answer is wrong...

    What was wrong? Thank you.
    Last edited by Jameson; April 26th 2006 at 06:25 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    I think you're close. Remember you're solving for a rate, not a distance. A is the only value in the triangle that's constant, so B and C are variables as the plane flies. You have used the law of cosines correctly, but keep B as a variable and differentiate to find the rate of change.

    C^2=4^2+B^2-2(4)(B)\cos{(120)}

    2C*\frac{dC}{dt}=2B*\frac{dB}{dt}-8\cos{(120)}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Mar 2006
    Posts
    705
    Thanks
    2
    Okay, I got what you are doing, but I don't understand how to solve for dC/dt

    The question is asked to find dC/dt when 3 mins after, so I will have find the value of B and C 3 mins later in order to find the rate of change of C.

    B after 3 mins is 72km, what is C, 5488km?
    Last edited by tttcomrader; April 26th 2006 at 08:48 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: September 16th 2009, 04:45 PM
  2. Help got exam tomorrow!
    Posted in the Calculus Forum
    Replies: 0
    Last Post: June 9th 2009, 10:06 PM
  3. Help please exam tomorrow!
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: April 23rd 2009, 10:55 AM
  4. Help please ^_^ exam tomorrow :(
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: February 23rd 2008, 05:08 PM
  5. Replies: 3
    Last Post: April 4th 2006, 04:27 AM

Search Tags


/mathhelpforum @mathhelpforum