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Homework Help: Find the ratio of maximum height to radius of planet

  1. Mar 6, 2010 #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 61 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 radius of the planet, h/R?

    2. Relevant equations
    1/2mv² = -Gmm/R
    Vf² = Vi² - 2gh

    3. The attempt at a solution
    1. 1/2mv² = -Gmm/R
    v² = -2Gm/R
    v = .61√(2Gm/R)

    2. Vf² = Vi² - 2gh
    0 = Vi² - 2gh
    Vi² = 2gh
    Vi = √2gh

    3. .61√(2Gm/R) = √(2Gh)
    .7442(Gm/R) = 2(Gmh/R²)
    .7442Gm = 2(Gmh/R)
    .7442 = 2h/R
    h/R = .3721

    Any thoughts or advice on the incorrect answer? Thanks in advance.
     
  2. jcsd
  3. Mar 7, 2010 #2

    ehild

    User Avatar
    Homework Helper

    You made two serious mistakes:

    i. You can not apply the formula Vf² = Vi² - 2gh when the height a projectile reaches is comparable with the radius of the planet.

    ii. "g" in the formula above is the free -fall acceleration at the surface of the planet, and entirely different from the universal gravitational constant G.

    Use the law of conservation of energy in the gravitational field of the planet.

    ehild
     
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