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Two dimensional projectile motion

  1. Apr 23, 2014 #1

    utkarshakash

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    1. The problem statement, all variables and given/known data
    A regular hexagon of side a=10√3 m is kept at horizontal surface as shown in the figure. A particle is projected with velocity V m/s at an angle θ from point k such that it will just touch the all four corners B,C,D,E. If O is the centre of hexagon and x-axis is parallel to horizontal and y-axis is perpendicular to AF and CD sides of hexagon then answer the following

    A) Velocity of projectile at maximum height

    3. The attempt at a solution
    Let k be the origin. R be the range of projectile
    Coordinates of B = (R/2 - a, a√3/2)
    Coordinates of C = (R/2 - a/2, a√3)
    Equation of trajectory : [itex]y=x \tan \theta \left(1-\dfrac{x}{R} \right) [/itex]

    Satisfying the above coordinates does not give me the right answer.
     

    Attached Files:

  2. jcsd
  3. Apr 23, 2014 #2
    I don't think your coordinates are correct. Can you show how did you find them? Its difficult to follow your working.
     
  4. Apr 23, 2014 #3

    utkarshakash

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    Let the mid-point of AF be T. KT=R/2. Drop a perpendicular from B to the line KAFL. Call it BW.
    AT=a/2. AW=acos60° = a/2. Thus, WT = a. x coordinate of B = KT-WT = R/2 - a.
    For y-coordinate, BW = asin60 = a√3/2. Similar approach can be followed to find to coordinates of C.
     
  5. Apr 23, 2014 #4

    ehild

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    R is not known. Determine the coordinates from the given side of the hexagon, in he suggested coordinate system (origin is at the centre of the hexagon).

    ehild
     
  6. Apr 23, 2014 #5
    Looks ok to me.

    Plugging in the coordinates, you get two equations, divide them to eliminate tan. Solve for R.
     
  7. Apr 23, 2014 #6

    utkarshakash

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    But then the equation of trajectory would need a transformation and it would be difficult to do that.
     
  8. Apr 23, 2014 #7

    ehild

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    The trajectory is a parabola, and you do not need the range. You need theta and V.

    And you need the coordinates anyway.

    ehild
     
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