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Projectile Motion: Determine v_0 to go over a fence

  1. Feb 4, 2016 #1
    1. The problem statement, all variables and given/known data
    You're the new home run hitter for a baseball team. Your job is to hit the ball over a fence D away and H high. For a given angle θ calculate the speed with which the ball must be hit v0 to go over the top of the fence.

    2. Relevant equations
    1. y = y0+(v0*sinθ)-½gt2
    2. x = v0*t*cosθ

    3. The attempt at a solution

    I tried using H as my y value from eq. 1 and D as my x value in eq. 2. I solved for v0 in eq. 2 (D/(t*cosθ)), then attempted to eliminate t by solving for it in equation 1 using the quadratic formula. Then I substituted the result into the D/(t*cosθ) equation.

    The result is a very bulky equation that I'm unsure is correct. A tutor said my reasoning was sound, and was unable to come up with a more simplified answer himself. What do you guys think? Am I even on the right track here?
  2. jcsd
  3. Feb 4, 2016 #2
    Yep, it's complicated.
  4. Feb 4, 2016 #3
    The problem, the answer, or both?
  5. Feb 4, 2016 #4
    The best double check is to plot the resulting parametric equations with real numbers and see if it clears the fence.
  6. Feb 4, 2016 #5


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    Your quoted equation for y is missing something. I assume that's just a typo.
    I assume H is the height relative to the point of impact, so y0=0.
    The only use of t here is to connect the horizontal and vertical motions, so I would start by obtaining a single equation relating x and y, with t absent.
    After that it does not look complicated to me. You can get a small simplification by using the formulae for sin(2θ) and cos(2θ).
    Please post your working.
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