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Two-Dimensional Motion

  1. Nov 6, 2009 #1
    A pitched ball is hit by a batter at a 40° angle and just clears the outfield fence, 96 m away. If the fence is at the same height as the pitch, find the velocity of the ball when it left the bat. Ignore air resistance. Velocity at 40°?

    Honestly I don't know how to do this. I have a whole assignment with problems just like this and I normally can do them but, I feel like I don't have enough information. I'd just like some help in trying to start this. Help, please?
     
  2. jcsd
  3. Nov 6, 2009 #2

    LCKurtz

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    Doesn't your book have equations like:

    [tex]y = -\frac {gt^2} 2 + v_y(0)t + y_0[/tex]

    [tex]x = v_x(0)t + x_0[/tex]

    and any examples? Put the origin at the point where the bat contacts the ball to get started.
     
  4. Nov 7, 2009 #3
    Yeah, the book has examples but, not for the problems like that one. I feel like the question doesn't give me enough information.
     
  5. Nov 7, 2009 #4
    Since the fence is at the same height as the pitch, let that be the x-axis. The ball's path is then a parabola; let the strike of the ball be the origin; that is one root and the other is where the ball just clears the fence at x = 96m. Together with the fact that the degree at which the parabola touches the axis is 40 degrees, this completely determines the parabola.
    Have you covered parametric equations, or the equation of the parabola on xy coordinates instead of yt coordinates?
    If not, look at the equations that LCKurtz posted and note that you can solve the second equation for t and thus get y in terms of x in the first equation. You also have both roots of the parabola, allowing you to solve for velocity components.
    If you don't feel comfortable with the parabola, you can also solve this as two equations in two unknowns.
     
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