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Math Help - Show that S and B will collide...

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    Show that S and B will collide...

    (In this question the unit vectors i and j are due east and north respectively.)

    At noon a ship S is 600m due north of an observation point O and a speedboat B is 120m due north of the same point. The ship S has a constant velocity of |7i+8j|ms^{-1} and the speedboat B has a constant velocity of |7i+24j|ms^{-1}.

    b). Show that S and B will collide and find the time when this collision occurs and the position vector of the point of collision.

    My attempt:

    600i + t(7i+8j) = 120i + t(7i+24j)

    From there I need to find what t equals. That would give me the time when they collide. I've tried rearranging the equation to get t on one side, I've even tried finding the magnitude of the component vectors, where 7i+24j would be 25, but I just can't work it out =\ . Please tell me how to work it out, and I will go from there.
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  2. #2
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    Quote Originally Posted by Viral View Post
    (In this question the unit vectors i and j are due east and north respectively.)

    At noon a ship S is 600m due north of an observation point O and a speedboat B is 120m due north of the same point. The ship S has a constant velocity of |7i+8j|ms^{-1} and the speedboat B has a constant velocity of |7i+24j|ms^{-1}.

    b). Show that S and B will collide and find the time when this collision occurs and the position vector of the point of collision.

    My attempt:

    600i + t(7i+8j) = 120i + t(7i+24j)

    From there I need to find what t equals. That would give me the time when they collide. I've tried rearranging the equation to get t on one side, I've even tried finding the magnitude of the component vectors, where 7i+24j would be 25, but I just can't work it out =\ . Please tell me how to work it out, and I will go from there.
    position vector equation should be ...

    600j + (7i+8j)t = 120j + (7i+24j)t


    in the x-direction ...

    7t = 7t (what does that say about their respective positions in the x-direction?)

    in the y-direction ...

    600+8t = 120+24t

    solve for t.
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