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Velocity at the midway point

  1. Jan 3, 2015 #1
    1. The problem statement, all variables and given/known data
    The velocity at the midway point of a ball able to reach a height y when thrown with a velocity v0 at the origin is:


    2. Relevant equations
    v2=v02+2ay

    3. The attempt at a solution
    I made y = 1/2 y and the simplified the equation to v=sqrt(v02+ay)
    But that is wrong because the answer is sqrt(v02/2)
    Why?
     
  2. jcsd
  3. Jan 3, 2015 #2

    TSny

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    See if you can continue to simplify your result. In particular, can you find a way to express ay in terms of v0?
     
  4. Jan 4, 2015 #3
    a = (v-v0)/t
    y = v0t+1/2 at2
    Substituting those don't seem to help enough
     
  5. Jan 4, 2015 #4

    TSny

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    In your first post, you stated the following useful equation: v2 = vo2 + 2ay.

    In your problem, y represents the height to which the ball will reach (i.e., the maximum height). When the ball reaches maximum height, what can you say about the value of v on the left side of the equation?
     
  6. Jan 4, 2015 #5
    Oh wow, then you get ay = - v02/2
    and then if you plug that back into my first equation, you get the answer.
    Wouldn't have thought of that. Thanks!
     
  7. Nov 12, 2015 #6
    Can you please explain more ?
     
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