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One dimensional motion problem

  1. Jun 11, 2009 #1
    1. The problem statement, all variables and given/known data
    Challenge Problem(2.96) from University Physics text book:
    In the vertical jump, an athlete starts from a crouch and jumps upward to reach as high as possible. Even the best athletes spend little more than 1.00s in the air (their "hang time"). Treat the athlete as a particle and let Ymax be his maximum height above the floor. To explain why he seems to hang in the air, calculate the ratio of the time he is above y/2 to the time it takes him to go from the floor to that height. You may ignore air resistance.

    2. Relevant equations
    constant acceleration equations: y=Y0 + V0t - 4.9t2....1
    V2y=V20y-2g(y-y0)......2

    3. The attempt at a solution
    Part 1(Time it takes him to go from floor to Ymax /2):
    ay= -g, origin at the floor, V0y=0, y=Ymax /2, y0=0

    so if i substitute these known quantities in the second equation, then for the velocity at the position Ymax /2 i am getting complex roots. Kindly inform me where i am going wrong.

    Thanks,
     
  2. jcsd
  3. Jun 11, 2009 #2
    Try using a positive value for g. Since when you ultimately calculate time, using a negative value would result in a negative value under the square root.

    Edit: Strike out what I said.
     
    Last edited: Jun 11, 2009
  4. Jun 11, 2009 #3

    Cyosis

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    No. if v0y=0 then how can he even get into the air? You can calculate what v0y is because you know what vymax is. What is vymax?
     
  5. Jun 11, 2009 #4
    Thanks Cyosis, I got it. since we know that Vymax is zero we can calculate the initial velocity of the part 2 which becomes the final velocity of part 1. am i right??
     
  6. Jun 11, 2009 #5

    Cyosis

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    Yep.
     
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