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Babynini

  • one year ago

A river is flowing due east at 8 mi/hr. A man heads his motorboat in the direction N30E in the river. the speed of the motorboat relative to the water is 12mi/hr a)express the true velocity of the motorboat as a vector b) find the true speed and direction of the motor boat.

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  1. Babynini
    • one year ago
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    @zepdrix free? (:

  2. Babynini
    • one year ago
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    @jim_thompson5910 whenever you're free, please! :)

  3. jim_thompson5910
    • one year ago
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    |dw:1434672450418:dw|

  4. jim_thompson5910
    • one year ago
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    Draw in a parallelogram |dw:1434672391987:dw|

  5. jim_thompson5910
    • one year ago
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    this vector, ie the resultant vector, is the boat's true path |dw:1434672449672:dw|

  6. Babynini
    • one year ago
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    oo ok

  7. Babynini
    • one year ago
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    Following so far

  8. Babynini
    • one year ago
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    and the resultant is w = u + v right?

  9. jim_thompson5910
    • one year ago
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    what is the vector component form for the vector pointing directly east (the river current)?

  10. Babynini
    • one year ago
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    emm v = 0i + 8j ?

  11. jim_thompson5910
    • one year ago
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    close

  12. jim_thompson5910
    • one year ago
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    that's pointing north though

  13. Babynini
    • one year ago
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    oops sorry v= 8i + 0j

  14. jim_thompson5910
    • one year ago
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    correct

  15. jim_thompson5910
    • one year ago
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    what is the boat's vector (ignore the current) ?

  16. jim_thompson5910
    • one year ago
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    hint: |dw:1434672891389:dw|

  17. Babynini
    • one year ago
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    Um..not sure

  18. jim_thompson5910
    • one year ago
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    z = x*i + y*j x = r*cos(theta) y = r*sin(theta) theta = 60 degrees r = 12

  19. Babynini
    • one year ago
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    x = 6 y = (12 sq3)/2

  20. jim_thompson5910
    • one year ago
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    or y = 6*sqrt(3)

  21. Babynini
    • one year ago
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    or y = 6 sq3

  22. jim_thompson5910
    • one year ago
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    yep

  23. Babynini
    • one year ago
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    haha yes

  24. jim_thompson5910
    • one year ago
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    so that's the boat's vector <6, 6*sqrt(3)>

  25. jim_thompson5910
    • one year ago
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    |dw:1434673336710:dw|

  26. jim_thompson5910
    • one year ago
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    |dw:1434673363432:dw|

  27. Babynini
    • one year ago
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    so is it = <14, 6 sq3>

  28. jim_thompson5910
    • one year ago
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    yes, that's u+v

  29. jim_thompson5910
    • one year ago
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    which is also the true velocity vector of the boat

  30. Babynini
    • one year ago
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    yaaay! Now part b :)

  31. jim_thompson5910
    • one year ago
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    true speed = |u+v| true direction = direction of vector u+v

  32. Babynini
    • one year ago
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    Direction = 2 sq76 ?

  33. Babynini
    • one year ago
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    or 4 sq19

  34. jim_thompson5910
    • one year ago
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    4*sqrt(19) is the magnitude of u+v so it is the true speed

  35. Babynini
    • one year ago
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    o right. Direction: (theta) = arctan( (6sq3)/14)

  36. Babynini
    • one year ago
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    so.. 36.58?

  37. Babynini
    • one year ago
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    but if we want to find it from x it would be that subtracted from 180 correct?

  38. Babynini
    • one year ago
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    sorry, I meant 90

  39. Babynini
    • one year ago
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    Which would be 53.41

  40. Babynini
    • one year ago
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    N53E

  41. jim_thompson5910
    • one year ago
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    yeah I'm getting theta = 36.58677555 so 90 - theta = 90 - 36.58677555 = 53.41322445

  42. Babynini
    • one year ago
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    Yay, it matches :)

  43. Babynini
    • one year ago
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    a) velocity of motorboat: <14, 6*sq3> b) Speed: 17.44 Direction: N53.4E

  44. jim_thompson5910
    • one year ago
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    everything looks good

  45. Babynini
    • one year ago
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    thank you

  46. jim_thompson5910
    • one year ago
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    yw

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