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he66666

  • 5 years ago

Grade 12 math: vectors as forces? Two tugs are towing a ship. The smaller tug is 15 degrees off the port bow, and the larger tug is 20 degrees off the starboard bow. The larger tug pulls twice as hard as the smaller tug. In what direction will the ship move? answer: 8.5 degrees to the starboard side I really don't get how you solve this question. Can someone please explain the solution?

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  1. anonymous
    • 5 years ago
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    So we denote force that small exert as x

  2. anonymous
    • 5 years ago
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    that mean larger boat exerts 2x maganitude of force

  3. anonymous
    • 5 years ago
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    Do you have a picture or diagram?

  4. amistre64
    • 5 years ago
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    you can add your vectors to get the direction of motion..right?

  5. amistre64
    • 5 years ago
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  6. amistre64
    • 5 years ago
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    as you can see, i added one vector to the end of the other, and where it ends up pointing is our new direction of travel

  7. he66666
    • 5 years ago
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    I stil don't understand.. how did it turn into a parallelogram? our teacher told us to use the position diagram and the vector diagram.. :S

  8. amistre64
    • 5 years ago
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    vectors can move around the graph; they arent anchored to one spot

  9. amistre64
    • 5 years ago
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    vectors are simply direction and magnitude with no regard to initial position....

  10. amistre64
    • 5 years ago
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    we add vectors by stacking them head to tail and drawing a new vector from the start to the end...

  11. he66666
    • 5 years ago
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    yes, but if it's two tugs towing a ship, shouldn't the diagram be a triangle with the two tensions?

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  12. amistre64
    • 5 years ago
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    it is, the initial positions are to the left and right of the ship; then i took one vetor and added it to the other to determine the direction of travel when both forces are applied

  13. he66666
    • 5 years ago
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    oh I understand now. So after I draw the parallelogram, what do I do?

  14. amistre64
    • 5 years ago
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    well, that gives you an idea of whats going on; the real eat is in deciphering the angles for the information they can give...

  15. amistre64
    • 5 years ago
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    one vector is twice the other, so we can use 1 and 2 as magnitudes....length of the vectors right?

  16. he66666
    • 5 years ago
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    so the length of the vectors represent tension?

  17. amistre64
    • 5 years ago
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    the length represent force, whatever you wanna call it :)

  18. he66666
    • 5 years ago
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    oh ok. sorry for asking so many questions, I'm not good at vectors :/

  19. amistre64
    • 5 years ago
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  20. amistre64
    • 5 years ago
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    lets start getting some sin and cos number to define these vector better....

  21. amistre64
    • 5 years ago
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    vector small = <cos15,sin15> vector large = <2cos20, 2sin20> you see why?

  22. amistre64
    • 5 years ago
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    vs=<.9659, .2588> vl = <1.8794, -.6840> now we add them like we did in the picture but this time its simply the numbers

  23. he66666
    • 5 years ago
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    Yes, i'm following

  24. amistre64
    • 5 years ago
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    .9659, .2588 1.8794, -.6840 ------------- <2.8453, -.4252> is the direction and length of our new vector

  25. amistre64
    • 5 years ago
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    we take the inverse tangent of these number to find the angle created....and hopefully its right :)

  26. amistre64
    • 5 years ago
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    |-8.499| = 8.499 we good with it? do you see what i did ?

  27. he66666
    • 5 years ago
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    yup :)

  28. amistre64
    • 5 years ago
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    <x,y> is what our new vector lloks like. y/x = tan(angle) tan^-1(y/x) = angle

  29. amistre64
    • 5 years ago
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    if theres another way to get to that, fine; but thats how id do it cause it works lol

  30. he66666
    • 5 years ago
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    Oh, I see. I get it now! thanks a bunch :D

  31. amistre64
    • 5 years ago
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    yw :)

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