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Projectile Fired Up A Hill

  1. Feb 6, 2008 #1
    the following problem is from the 5th edition of Thorton and Marion's "Classical Dynamics"
    ch.2 problem 14 p.92

    The problem statement, all variables and given/known data
    A projectile is fired with initial speed v_0 at an elevation angle of alpha up a hill of slope beta (alpha > beta).

    (a) how far up the hill will the projectile land?
    (b) at what angle alpha will the range be a maximum?
    (c) what is the maximum angle?

    The attempt at a solution
    apparently this has been a stumper in former classical mechanics classes, but here was as far as i got:

    i broke down the components of the forces into x and y
    x-component:
    a_x=0 integrating -->
    v_x = v_0 cos(beta) integrating -->
    x = v_0 t cos(beta)

    a_y = -g integrating -->
    v_y = -gt + v_0 sin (alpha - beta) integrating -->
    y = ( -gt^2 / 2 ) + v_0 sin (alpha - beta)


    the answer in the back of the book for part (a) is:
    d = (2 v_0^2 cos(alpha) sin(alpha-beta) ) / (g cos^2(beta))

    any idea how to get from the components to the answer?
     
  2. jcsd
  3. Feb 7, 2008 #2

    Hootenanny

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    Hint: The distance is the magnitude of the position vector.
     
  4. Sep 19, 2009 #3
    I too am having trouble with this problem. In the book, they use Taylor expansions in order to find the flight time T and put in back into the range equation. However, they have the luxury of letting y = 0 because the trajectory is a simple parabola. We don't have the same situation here. y doesn't equal zero, y = beta*range.
     
  5. Sep 20, 2009 #4
    I have no idea how we're supposed to get things like cos([tex]\beta[/tex])
     
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