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Dynamics f=ma

  1. Feb 3, 2012 #1
    1. The problem statement, all variables and given/known data

    A baseball slugger connects with a pitch 4 ft above the ground. The ball heads toward the 10-ft-high center-field fence, 455 ft away. The ball leaves the bat with a velocity of 125 ft/s and a slope of 3 vertical to 4 horizontal. Neglecting air resistance, determine whether the ball hits the fence (if it does, how high above the ground?) or whether it is a home run (if it is, by how much does it clear the fence?).

    2. Relevant equations

    F=ma (Euler form)

    3. The attempt at a solution
    The book gives the answer as home run, clears fence by 2 ft.

    -mgj = m[ x2i+y2j+z2k) Note that i,j,k are unit vectors, and x2, y2, and z2 means double dot or acceleration.

    -g = y2
    0 = x2

    y1 = -gt + C [C=125*(3/5)] => y1 = -gt + 75 (y1 is y dot or velocity)
    y = (-gt^2)/2 + 75t + C [C=4] => y = -(gt^2)/2+75t+4

    x1 = C [C=125*(4/5)] => x1 = 100
    x = 100t + C [C=0 because no movement in x direction at t = 0] = > x=100t

    Got these equations, then plugged in 455 ft into x=100t to get t=4.55s. So at 4.55s the ball would reach the fence. As to how high it will be, plug t=4.55 into the y equation, and my answer is 243 ft. The fence is 10 ft, so it clears it by 233 ft. But the book's answer is 2 ft. I know I screwed up somewhere, but I can't see it. Any help would be appreciated.
     
  2. jcsd
  3. Feb 3, 2012 #2

    tiny-tim

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    Homework Helper

    hi xzibition8612! :smile:

    (btw, pleeease don't write x1 x2 etc, write x' x'' :wink:)

    did you use 9.81 for g, or 32 ?
     
  4. Feb 3, 2012 #3
    wow :cry:
     
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