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Homework Help: Projectile Launch - Earth's Radius

  1. Mar 21, 2005 #1
    The answer that the book gives for the question:
    What is the launch speed of a projectile that rises above the Earth to an altitude equal to the Earth's radius? Ans. 7.91 km/s

    Now I have the question:
    What is the launch speed of a projectile that rises above the Earth to an altitude equal to three times the Earth's radius?

    So I use:
    [tex]v_{f} = \sqrt(((2GM_{e})/(4R_{e}))[/tex]

    Note:
    G = 6.67x10^-11
    Me = 5.97x10^34 kg
    Re = 6.37x10^6 m

    The resulting answer I get is 5.59 km/s. That equation works for an altitude equal to the earth's radius, but not for my problem. Why not? What am I doing wrong?
     
  2. jcsd
  3. Mar 21, 2005 #2
    Possibly using 4R_{e} instead of 3R_{e}?
     
  4. Mar 21, 2005 #3

    Andrew Mason

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    Science Advisor
    Homework Helper

    The correct energy equation is:

    [tex]KE = \Delta PE = GMm(\frac{1}{R_{i}}-\frac{1}{R_{f}})[/tex]

    [tex]v_i= \sqrt{2GM(\frac{1}{R_e}-\frac{1}{4R_e})}[/tex]

    BTW, the mass of the earth is 5.97x1024 kg.

    AM
     
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