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Math Help - vector word problem

  1. #1
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    vector word problem

    Hi guys,

    the question i am workinflg on is:

    A ship is required to travel south at a speed of 20km/h. There is a current of 6km/h from the southwest

    I am trying to work out the direction the ship must head to compensate for the current and the speed the ship must travel in order to achieve its speed of 20km/h.

    I have started by looking at the vector current and calculating its i and j components which i found to be each 6/sqrt2.

    I am a bit stuck now and would really appreciate some help, thanks!
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  2. #2
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    Re: vector word problem

    Let \vec{i} be the unit "east" vector and let \vec{j} be the unit "north" vector. The ship's velocity (or any vector) can be written a\vec{i}+ b\vec{j}. You are given that the desired velocity is -20\vec{j} and you have correctly calculated that the current's velocity is 3\sqrt{2}\vec{i}+ 3\sqrt{2}\vec{j}. Those must add to the desired velocity. Solve a\vec{i}+ b\vec{j}+ 3\sqrt{2}\vec{i}+ 3\sqrt{2}\vec{j}= (a+ 3\sqrt{2})\vec{i}+ (b+ 3\sqrt{2})\vec{j}= 0\vec{i}- 20\vec{j}.
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  3. #3
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    Re: vector word problem

    Hi sorry, where does 3sqrt2 come from ( i got 6/ sqrt2 for i and j from the 45 degree triangle formed by the current vector)
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  4. #4
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    Re: vector word problem

    Have you never heard of "rationalizing the denominator"?
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  5. #5
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    Re: vector word problem

    oh okay thanks very much for your reply
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