Results 1 to 3 of 3

Math Help - World Problem Involving Derivatives

  1. #1
    Newbie
    Joined
    Mar 2013
    From
    Canada
    Posts
    3

    World Problem Involving Derivatives

    The World Problem:

    At 9:30am, one ship was 65 miles due east from a second ship. If the first ship sailed west at 20 miles per hour and the second ship sailed southeast at 30 miles per hour, when were they closest together?

    What I Have So Far:

    1st ship coordinates: (0,0)
    2nd ship coordinates: (-65,0)

    x2+x2=(30t)2
    x = 15\sqrt{2}t

    Letting time be 't' in hours since 9:30am :
    1st ship coordinates: (-20t,0)
    2nd ship coordinates: ( -65 + 15\sqrt{2}t, -15\sqrt{2}t)

    Not sure where to go where to go from here... Can anyone help me out?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2009
    Posts
    660
    Thanks
    133

    Re: World Problem Involving Derivatives

    If the distance between the two boats is D, then

    D^{2} = (-20t+65-15t\sqrt{2})^{2}+(15t\sqrt{2})^{2}.

    For minimum D, differentiate this (no need to take the square root), and equate the result to zero.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2013
    From
    Canada
    Posts
    3

    Re: World Problem Involving Derivatives

    So then would it be..

    (1300+600\sqrt{2}) t^2 - (2600 + 1950\sqrt{2}) t + 4225
    2(1300+600\sqrt{2})t = 2600 + 1950\sqrt{2}
    t = 1.25

    Which makes it 10:45am

    Thank you so much for the guidance!!
    Last edited by aprilsauce; March 10th 2013 at 01:31 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: September 22nd 2012, 06:15 PM
  2. Replies: 1
    Last Post: July 5th 2012, 07:15 PM
  3. thought problem involving derivatives
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 12th 2008, 08:24 PM
  4. Word problem involving partial derivatives
    Posted in the Calculus Forum
    Replies: 0
    Last Post: March 4th 2008, 05:04 PM
  5. Replies: 3
    Last Post: May 29th 2006, 12:12 PM

Search Tags


/mathhelpforum @mathhelpforum