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Math Help - Ships when ill they meet?

  1. #1
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    Ships when ill they meet?

    Startng point 0,0
    1 ship has the time T=0 posision 0.5 miles east of a point and 0,4north
    the boat is sailing with the speed 0.8/hour with the dirction 55 degrees

    Another boat have this speed

    (xt),y(t))=(-2,236t+5,5;4.472t+1,o)

    -What is the speed of th lastboat and in wich direction( degrees)
    -And will h boats ever meet? if so in wich point

    Sry 4 my english
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  2. #2
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    Quote Originally Posted by Nuke View Post
    Startng point 0,0
    1 ship has the time T=0 posision 0.5 miles east of a point and 0,4north
    the boat is sailing with the speed 0.8/hour with the dirction 55 degrees

    Another boat have this speed

    (xt),y(t))=(-2,236t+5,5;4.472t+1,o)

    -What is the speed of th lastboat and in wich direction( degrees)
    -And will h boats ever meet? if so in wich point

    Sry 4 my english
    Make a rough sketch!

    Construct a coordinate system with the y-axis pointing North and the x-axis pointing East. You must transform the courses into angles with respect to the x-axis!

    The way of the ship is a straight line:

    \vec s = (0.5, 0.4)+t \cdot (0.8 \cdot \cos(35^\circ), 0.8 \cdot \sin(35^\circ))

    Expand the values in the direction vector and use rounded decimals:

    \vec s = (0.5, 0.4)+t \cdot (0.6553, 0.4589)

    The way of the boat (the 2nd vessel!) is:

    \vec b = (5.5, 1)+r\cdot(-2.236,  4.472)

    The norm of the direction vector represents the speed of the boat:

    v=\sqrt{(-2.236)^2+ ( 4.472)^2}=5.0\ kn

    The angle with respect to the x-axis is:

    \tan(\phi)=\dfrac{4.472}{-2.236} = -2~\implies~\phi\approx -63.435^\circ

    Since the direction vector is pointing into the 4th quadrant the boat is heading 270^\circ+63.435^\circ = 333.435^\circ

    To answer the second question calculate the point of intersection between the two lines:

    \left|\begin{array}{rcl}0.5+0.6553t&=&5.5-2.236r \\ 0.4+0.4589 t&=& 1+4.472r\end{array}\right.

    I've got t = 5.99 and r = 0.48

    And what does that mean?
    Attached Thumbnails Attached Thumbnails Ships when ill they meet?-kollisionskurs.png  
    Last edited by earboth; May 27th 2009 at 04:10 AM. Reason: sketch added
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