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M1 Vectors help

  1. Sep 9, 2007 #1

    I would really appreciate it if someone could please explain to me part c of this M1 level vector question as I am really stuck.

    Two trains A and B leave the same station, O, at 10 a.m. and travel along straight horizontal tracks. A travels with constant speed 80 Km/h due east and B travels with constant speed 52 km/h in the direction (5i + 12j) where i and j are unit vectors due east and due north respectively.

    (a) Show that the velocity of B is (20i + 48j) km/h.

    I got this part ok.

    (b) Find the displacement vector of B from A at 10:15 a.m.

    I got this as (15i + 12j).

    Given that the trains are 23 km apart t minutes after 10 a.m.

    (c) find the value of t correct the nearest whole number.

    Thank you.

  2. jcsd
  3. Sep 9, 2007 #2


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    Shouldn't part b) be 15i - 12j ?

    For part c) you need the displacement vector from B to A (or A to B) in terms of t. Then set the magnitude of that vector equal to 23km and solve for t.
  4. Sep 9, 2007 #3
    Thanks for your help.

    I got 15 hours.

    Is this correct?

  5. Sep 9, 2007 #4


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    No. Can you show your calculations?
  6. Sep 9, 2007 #5

    I got that the position vector of A in terms of t is 80ti and that the position vector of B in terms of t = (20ti + 48tj).

    I then subtracted B from A and got (60ti - 48tj).

    23^2 = 529 and so the square root of ((60t)^2 - (48t)^2)) = 529

    1296t^2 = 279841

    t = 14.69444444 hours or 15 hours to the nearest whole number.

  7. Sep 9, 2007 #6


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    It should be [tex]\sqrt{{60t}^2 + {(-48t)}^2} = 23[/tex]

    Remember that when getting the magnitude of the vector, to take the entire component... ie 60ti -48tj = 60ti + (-48t)j... so you need to take (60t)^2 + (-48t)^2 under the square root.

    Then you should square both sides and simplify and get

    5904t^2 = 529

    But this gives the time in hours. The question asks for the minutes, so convert the number you get here into minutes...
  8. Sep 9, 2007 #7
    Thanks so much for your help.

    I got 18 minutes.

  9. Sep 9, 2007 #8


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    Yup, that's it. no prob.
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