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Speed problem

  1. Nov 3, 2009 #1
    1. The problem statement, all variables and given/known data
    At what speed would a 70-kg high jumper have to leave the ground in order to raise his body up to a height of 1.60 m

    Acceleration due to gravity: 9.8 m/s^2 [down]
    2. Relevant equations

    Kinetic Energy = 0.5(mass)(velocity^2)
    Gravitational Potential Energy = (mass)(accleration due to gravity)(height)

    3. The attempt at a solution
     
  2. jcsd
  3. Nov 3, 2009 #2
    Answer is 5.6 m/s but i dont know how to get it
     
  4. Nov 3, 2009 #3
    Because only conservative forces are acting upon the system:
    Change in Potential Energy + Change in Kinetic Energy = 0
    Change in potential energy = mg(hf-hi)
    Change in kinetic energy = .5(m)(vf2-vI2)
    vf is zero because the jumper just reaches the maximum height of 1.6 meters. hi is also zero because the jumper starts on the ground. hf is 1.6 meters. Substituting, we obtain
    -1097.6 + 35vi2 = 0 (Because gravity points down, it has a value of -9.8 m/s20
    Solving for v results in the answer of 5.6 m/s.
     
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