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How high does it go?

  1. Jun 5, 2009 #1
    1. The problem statement, all variables and given/known data
    A huge cannon is assembled on an airless planet. The planet has a radius of 6.00×106 m and a mass of 3.06×1024 kg. The cannon fires a projectile straight up at 5270 m/s.
    An observation satellite orbits the planet at a height of 4103.30 km. What is the projectile�s speed as it passes the satellite?


    2. Relevant equations
    K=mv^2/2
    U=-GMm/r



    3. The attempt at a solution
    Initially: Ki and Ui are both present
    Finally: Ki and Uf are both present again
    CORRECT?
    so i have the equation
    Ki-Ui=Kf-Uf
    wanting to solve for velocity at a certain point Uf actually is GMm/(R+H)
    CORRECT?
    So then I solved for Vf and get .......
    squareroot (2(Ki-Ui+Uf)/m)

    Then i plug and go....WHY ISN'T WORKING
     
  2. jcsd
  3. Jun 5, 2009 #2

    LowlyPion

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    You seem to have the basic idea.

    Kinetic energy at firing + potential energy gravity at surface = potential energy at satellite + kinetic energy of projectile.
     
  4. Jun 5, 2009 #3
    after plugging in the KE and PE equations i came up with......-2(-.5Vi^2+GM/R-GM/(R+h))
    square root of the whole thing.
     
  5. Jun 5, 2009 #4
    so instead of using the mass of the planet i should use mass of the sataellite?

    EDIT: I don't have the mass of the satellite so I believe I have it set up right.
     
  6. Jun 5, 2009 #5

    LowlyPion

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    No. Of course not.

    The Mass of the Planet and G give you a way to figure your potential energy ...

    U = -GM/r

    So ...

    at surface U = the above.
    at the satellite U = -GM/(r+h)

    (Don't forget the sign.)
     
  7. Jun 5, 2009 #6
    So then the way I set it up is right?
     
  8. Jun 5, 2009 #7

    LowlyPion

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    So long as you have also accounted for the potential energy at the surface as well.
     
  9. Jun 5, 2009 #8

    D H

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    You forgot that the satellite is in orbit. It's moving, too.
     
  10. Jun 5, 2009 #9
    I attached my equation.
     

    Attached Files:

  11. Jun 5, 2009 #10
    you can't just assume it isn't moving?
     
  12. Jun 5, 2009 #11

    LowlyPion

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    I don't think they are asking for the speed relative to the satellite.

    Merely the speed at the height (radius) of the satellite's orbit.
     
  13. Jun 5, 2009 #12
    thats what I figured. I figured that they just wanted the distance. Is my equation correct that i attached a few posts back?
     
  14. Jun 5, 2009 #13

    LowlyPion

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    Looks like the - in front of the 2 is not useful.

    I would examine they way you treated the mass of the projectile ... as a suggestion.
     
  15. Jun 5, 2009 #14
    The mass should cancel. i meant to erase it, and the 2 shouldn't be negative. I jsut worked through that equation and it said the answer is wrong.
     
    Last edited: Jun 5, 2009
  16. Jun 5, 2009 #15

    LowlyPion

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    Not in the equation you supplied.
     
  17. Jun 5, 2009 #16
    Opps that is my bad, I knew it canceled in my mind but when I re wrote it i forgot to cancel it even though I canceled the others.

    EDIT: WHen i worked through it, i didn't use the negative or the mass and it was wrong
     
  18. Jun 5, 2009 #17
    Has this question been resolved?
     
  19. Jun 5, 2009 #18

    LowlyPion

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    Maybe show your work? Perhaps you have a simple error?
     
  20. Jun 5, 2009 #19
    Wouldn't it just be easier to use [tex]S(t)=-gt^{2}+V_{o}t+h_{o}[/tex]?
     
  21. Jun 5, 2009 #20

    D H

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    No. That equation assumes a uniform gravity field.
     
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