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2-D Motion Conceptual Problem

  1. Oct 13, 2010 #1
    1. The problem statement, all variables and given/known data
    A ball is thrown horizontally from the top of a cliff with an initial Vo(at t=os). At any moment , its direction of motion makes an angle θ to the horizontal.

    1)Derive a formula for θ as a function of time, t, as the ball follows a projectile's path.

    2. Relevant equations

    3. The attempt at a solution
    components: Vx=Voxcosθ Vy=Voysinθ

    then i plugged the x component to find t:Vx=x/t.... t=x/(Voxcosθ)

    next i plugged t into a y position function Y=Yo+Voyt+1/2at^2

    0=h+(Voysinθ )(x/Voxcosθ)+(1/2*-9.8*(x/Voxcosθ)^2)

    this be correct because if u were given all of the initial heights and velocities the only variable left to solve for would be θ, giving you your answer right?
  2. jcsd
  3. Oct 13, 2010 #2


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    That's a pretty long equation. The horizontal velocity is always constant: v_x = v_ox.
    The vertical velocity is just v_y = gt.
    You can solve for theta as a function of t using basic trig properties of a right triangle.
  4. Oct 14, 2010 #3
    hey thanks, but u can only solve for theta using trig for a 1-d motion problem, but in 2-d the object follows a parabolic path so its velocity must be broken into components.

    the t=x/v_o cos(theta) gives you time which you plug in to the y position function, which accounts for the parabolic path.

    if anybody else knows what to do, any help would be aprreciated
  5. Nov 21, 2010 #4
    Does anybody else know how to solve this, I am really curious what the correct procedure is....
  6. Nov 21, 2010 #5
    If it helps you, I would start by sketching out a graph showing the function of time (Y) and its relationship to t. You can completely ignore X since it will have nothing to do with how quickly Y changes. Y is only a function of time.

    From there on out, follow PhanthomJay's suggestions.
  7. Nov 22, 2010 #6
    After re-reading your OP, I'm sorry for replying with an incorrect response. I misunderstood your question (whoops!) :redface:
    Use the equations for your X and Y components of your velocity and work out θ using trig.
  8. Dec 5, 2010 #7
    no worries Condensate =P.. and ok i will try that when it comes around to AP review time, thanks for your help.
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