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Equations of motion ( vectors )

  1. Jun 6, 2013 #1
    1. The problem statement, all variables and given/known data

    Two particles move near the surface of the earth with u. acc 10 m/s^2 towards the ground . At the initial moment , the particles were located at one point in space and moved with velocities 3m/s and 4 m/s in opposite directions . Find the distance between the particles when their velocity vectors are mutually perpendicular .

    2. Relevant equations
    s = ut + 1/2 at^2


    3. The attempt at a solution

    the trajectory of the particles should form a half - ellipse .

    That's as far as i got , how should i relate the mutually perpendicular thing ??
     
  2. jcsd
  3. Jun 6, 2013 #2

    mfb

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    No.
    You can work with a homogeneous gravitational field here (same 10m/s^2 downwards everywhere). How do the paths look like? Can you write them as vectors?
     
  4. Jun 6, 2013 #3
    As they have the same origin and are moving in opposite directions , while one's velocity is greater under uniform gravitation , Their paths together should form a half ellipse . :/
     
  5. Jun 6, 2013 #4

    mfb

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    How does the path of the first object look like?
    How does the path of the second object look like?

    There is no way to combine them to a part of an ellipse, even if an ellipse can look a bit similar.
     
  6. Jun 6, 2013 #5
    so it will not form an ellipse , how should i solve this ?
     
  7. Jun 6, 2013 #6

    mfb

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    With the hints I gave in my posts?

    After time t, what are the horizontal and vertical velocities of the objects?
    What does "orthogonal" mean for vectors?
     
  8. Jun 6, 2013 #7
    Since there is no force in the horizontal direction,velocity changes only in the vertical direction.Assume after some time t they(velocity vectors) subtend some angles(α and β) with the horizontal.Since both the vectors should be perpendicular,derive a relation and solve.

    Hope this hepls
     
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