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Particle Shot Tangentially to Surface

  1. Oct 19, 2011 #1
    1. The problem statement, all variables and given/known data
    A particle mass m is shot tangentially to the surface of a planet mass M radius R0 at 3/4 escape velocity. Determine the maximum radius the particle achieves from the center of the planet


    2. Relevant equations
    Escape Velocity : √(2GM/r)
    Energy due to Gravity : -GMm/r2
    F=ma
    Angular Force : F=mv2/r
    Conservation of Angular Momentum : L = r x p or L=mvr



    3. The attempt at a solution
    Honestly - the beginning of the attempt is where I'm having the issue = I can't decide if I want to use conservation of energy, conservation of angular momentum.

    My thought process tells me alright, the particle is shot at a velocity v0 (3/4 escape velocity). This particle has a force acting upon it - the force due to gravity. I can picture exactly what happens to the particle. it won't be shot out fast enough to reach orbit, it reaches a maximum radius r, and then in a parabolic trajectory falls back down to the planet.

    Quite honestly - I feel like it should be a very simple solution, I just can't wrap my head around it. Perhaps a tip to start will give me the momentum to find the solution.

    Thanks!
     
  2. jcsd
  3. Oct 20, 2011 #2

    vela

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    Centripetal force, not angular force (whatever that means).
    L=mvr sin θ
    You don't need to choose. You have to use both.
    Elliptical trajectory, not parabolic.
     
  4. Oct 20, 2011 #3
    Thank you!

    I used conservation of energy

    1/2mvo2-C/A=1/2mvf2-C/A

    For vf I used conservation of angular momentum to put it into terms of vi

    Thanks again!
     
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