Results 1 to 2 of 2

Thread: Calculus again!!!

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    5

    Calculus again!!!

    A ship is sailing due north at 12 kn when it observes another ship dead at a distance of 15 n. mi. The second ship is sailing due east at 9 kn. What is the closest distance of approach of the two ships?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by Raina View Post
    A ship is sailing due north at 12 kn when it observes another ship dead at a distance of 15 n. mi. The second ship is sailing due east at 9 kn. What is the closest distance of approach of the two ships?
    immagine these two boats on a coordinate system. The first boat is at
    (0,-15) and the is at the origin.

    the coordinate of the 1st boat is given by the equation

    $\displaystyle (0,12t-15)$

    and the coordinate of the 2nd is

    $\displaystyle (9t,0)$

    We can find the distance between using the pythagorean theorem.

    $\displaystyle d^2=(0-9t)^2+((12t-15)-0)^2$

    $\displaystyle d=\sqrt{225t^2-360t+225}$

    $\displaystyle d=3\sqrt{25t^2-40t+25}$

    taking the derivative we get

    $\displaystyle d'=\frac{3(25t-20)}{\sqrt{25t^2-40t+25}}$

    setting the numerator equal to zero we get

    $\displaystyle 0=3(25t-20) \iff 0=25t-20 \iff 20 =25t \iff t=\frac{4}{5}$

    $\displaystyle d=3\sqrt{25(\frac{4}{5})^2-40(\frac{4}{5})+25}$

    $\displaystyle d=3\sqrt{16-32+25}=3\sqrt{9}=9$

    Yeah!!

    I hope this helps
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Dec 13th 2011, 09:11 PM
  2. Replies: 2
    Last Post: Jun 25th 2010, 10:41 PM
  3. Replies: 1
    Last Post: Feb 11th 2010, 07:09 AM
  4. Calculus III But doesn't require Calculus :)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Jun 19th 2009, 04:23 PM
  5. Replies: 1
    Last Post: Jun 23rd 2008, 09:17 AM

Search Tags


/mathhelpforum @mathhelpforum