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Homework Help: Ratio of max height of a projectile to planet radius

  1. Jan 12, 2009 #1
    1. The problem statement, all variables and given/known data

    Hint:Disregard any dissipative effects of the atmosphere of the planet.
    A projectile is launched from the surface of a planet (mass M, radius R)
    with a launch speed equal to 60 percent of the escape speed for that planet.
    The projectile will rise to a maximum height and fall back to the surface of
    the planet.

    What will be the ratio of its maximum height above the surface to the radius of the
    planet, h/R?

    2. Relevant equations

    escape speed:
    KE = E(gravity)
    1/2 mv^2 = (GMm)/R
    F/m = a
    a(gravity) = GM/R^2

    3. The attempt at a solution

    1/2 mv^2 = (GMm)/R
    v(escape) = (2GMm)/R
    v=sqrt((2GM)/R)
    vi = 0.6 sqrt((2GM)/R)

    vf^2 = vi^2 - 2gh
    0 = 0.72GM/R - 2(GM/R^2)h
    2(GM/R^2)h = 0.72GM/R
    h/R = 0.36
     
  2. jcsd
  3. Jan 12, 2009 #2
    Sorry I reworked this problem by myself and I solved it!
     
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