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Homework Help: I need help with this question about vectors

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  1. Dec 24, 2017 #1
    1. The problem statement, all variables and given/known data
    At noon two boats P and Q have a position vector (i+7j)km and (3i+8j)km respectively to the origin O.
    i and j are unit vectors in direction to East and north respectively
    P is moving south east at 5√2 km/h and Q is moving at a constant velocity of (6i+5j) km/h
    At time t after noon the position vectors of P and Q with respect to O are p km and Q km
    a) show that the velocity of P is ( 5i + 5j)
    b) find the time to the nearest minute when Q is north east of P

    2. Relevant equations
    Phythogorus theorum a^2 = b^2 + c^2


    3. The attempt at a solution
    I have done part a)
    Where if the velocity is (5i+5j), then if you use phythogorus theorum where √(5^2+5^2) I get 5√2

    I don't know how to do part b)
     
  2. jcsd
  3. Dec 24, 2017 #2

    PeroK

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    Have you drawn a diagram?
     
  4. Dec 24, 2017 #3

    LCKurtz

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    The red quotes seem inconsistent.
     
  5. Dec 24, 2017 #4

    phinds

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    Yeah. What he said.

    @lioric discussing this kind of problem without a vector diagram is a waste of time.
     
  6. Dec 24, 2017 #5
    Yes I have drawn a diagram
     
  7. Dec 24, 2017 #6

    phinds

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    Uh ... and do you plan to share it with US? You ARE asking us to discuss it after all.
     
  8. Dec 24, 2017 #7
    But my main problem is figuring out the wording of the question
    Is the question asking me to find the time when Q is at a bearing of 45 degrees of P?
     
  9. Dec 24, 2017 #8

    phinds

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    What does "North East" mean?
     
  10. Dec 24, 2017 #9
    East is 90 degrees from North
    North east is the bisection of that
    It's the line equidistant from the East and the north
    The angle is 45 degrees from north
     
  11. Dec 24, 2017 #10

    phinds

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    There are two lines that are 45 degrees from North. Yes, I DO know what you mean but my point is that without a vector diagram, again, this discussion is useless.
     
  12. Dec 24, 2017 #11

    LCKurtz

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    @lioric: Are you ever going to respond to post #3 with a correct statement of the problem?
     
  13. Dec 24, 2017 #12

    phinds

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    AND a vector diagram !
     
  14. Dec 24, 2017 #13
    What can I say about what the red quotes say? It's what the question said. Word to word
     
  15. Dec 24, 2017 #14
    I have drawn the diagram
    And I can solve the problem when I'm sure about the north east part
    I just need to know the exact meaning of that
    Just clearing my doubts
     
  16. Dec 24, 2017 #15

    LCKurtz

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    Do you understand that the direction and vector I quoted in red do not agree?
     
  17. Dec 24, 2017 #16

    phinds

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    He might have figured that out if he had done a correct vector diagram, which is one reason I keep telling him to do one (AND show it to us so we can help)
     
  18. Dec 25, 2017 #17
    Sorry that's a typo
    It's 5i-5j
    Sorry
     
  19. Dec 25, 2017 #18
    At noon two boats P and Q have a position vector (i+7j)km and (3i-8j)km respectively to the origin O.
    i and j are unit vectors in direction to East and north respectively
    P is moving south east at 5√2 km/h and Q is moving at a constant velocity of (6i+5j) km/h
    At time t after noon the position vectors of P and Q with respect to O are p km and Q km
    a) show that the velocity of P is ( 5i - 5j)
    b) find the time to the nearest minute when Q is north east of P

    This is the correct one
     
  20. Dec 25, 2017 #19
  21. Dec 25, 2017 #20

    LCKurtz

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    That and the now changed original position of Q. So now you can show us how you calculate Q and P's positions at time t. Then think about what must be true about Q-P for Q to be northeast of P.
     
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