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Projectile motion and initial speed

  1. Oct 17, 2009 #1
    1. The problem statement, all variables and given/known data

    From a height of 23 m, a ball is thrown horizontally. If it hits the ground with a speed that is three times its initial speed, what is the initial speed?

    vertical: a = -9.8, x = -23, t = ?, V0=?, V = 3V0
    horizontal: ?
    x is displacement

    2. Relevant equations
    Possibly relevant:
    V = Vo + at
    x-x0 = Vot + .5at2
    x-x0 = Vt - .5at2
    x-x0 = .5(V0+ v)t
    V2 = V02 + 2a(x-x0)

    3. The attempt at a solution
    Seems simple, but I have tried and cannot do this problem. Seems like there is not enough info.

    Solving the system of the following equations for vertical motion
    x-x0 = Vot + .5at2
    x-x0 = Vt - .5at2
    found that t = 2.1447, but I am not sure if this is correct. After that I just didn't know what to do. For horizontal movement, it seems like there is only time and the fact that the final velocity is 3 times the initial velocity.
     
  2. jcsd
  3. Oct 17, 2009 #2
    Your time for t is basically correct, though the number I got is slightly off. I get 2.17 for some reason.

    Using t, you can also find the final velocity in the y direction.

    After that, it's simple vector algebra. You know the Vfx vector and the Vfy vector. You know that the Vf vector is 3 times the Vox vector.

    So, you have enough information. Just set up the vectors.
     
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