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Energy Conservation applied to Earth's surface

  1. Nov 9, 2014 #1
    1. The problem statement, all variables and given/known data
    With what initial speed must an object be projected vertically upward from the surface of Earshot rise to a maximum height equal to Earth's radius? (neglect air resistance.) Apply energy conservation.

    2. Relevant equations
    ##E_{k_1}+E_{g_1}=E_{k_2}+E_{g_2}##, however since ##E_{g_1}=0## and ##E_{k_2}=0##,
    the equation is ##E_{k_1}=E_{g_2}##.
    ##E_{k_1}=\frac{mv^2}2##
    ##E_{g_2}=mgh##

    3. The attempt at a solution
    ##\frac{mv^2}2=mgh##
    ##v=\sqrt{2gh}##
    I know that the maximum height of the object is ##6.38*10^6 m##
    I do not know if this is the right formula that i am using because i get the wrong answer.
    The answer is supposed to be 7.91*10^3 m/s.
     
  2. jcsd
  3. Nov 9, 2014 #2

    gneill

    User Avatar

    Staff: Mentor

    mgh for gravitational PE only applies to bodies close to the surface of the Earth. Since this problem involves a distance that is double the Earth's radius you should revert to Newton's general formula.
     
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