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Bullet trajectories and Newton's Principia

  1. Feb 27, 2012 #1
    1. The problem statement, all variables and given/known data

    Newton's Principia suggested that if you fire a cannon from a high mountain it could fall, circle the earth, or fly away depending on how hard it was fired. Describe how this compares to bullet trajectories. What is the major difference with this trajectory? (for visualizing, see: http://galileoandeinstein.physics.virginia.edu/more_stuff/Applets/newt/newtmtn.html [Broken])

    3. The attempt at a solution
    Okay, with this problem I get that if you fire a cannon it could react this way , due to the fact the cannonball would a) succumb to gravity b) get caught betweens earths gravity field and begin to orbit or, C) would fly off into space in accordance to Newtons law of motion.

    What I don't get is how this compares to bullet trajectory. As far as I understand this would be the same case for a bullet trajectory, with the only difference being F=ma. (please correct me if I am wrong here)

    but as this is a kinematics section of a course, it seems that the force answer was not the correct one. Can any one explain the similarities and differences in terms of kinematics, not force or circular motion (if possible) as I am struggling to grasp this in kinematic terms.

    thanks in advance,
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Feb 27, 2012 #2

    Delphi51

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    The force of gravity should have the same effect on the bullet as on the cannonball.

    According to the picture, the cannon is always fired horizontally.
    A bullet fired near the surface of the earth usually is angled upward, even when aimed at a target at the same height. Could that be the "major difference"? Another factor is air resistance, much less up at mountain height.
     
  4. Mar 2, 2012 #3
    hmm yes I think that may be part of it. I still just dont feel totally satisfied with that answer. I just feel as though something is missing. maybe I am just trying to complicate the matter.
     
  5. Mar 2, 2012 #4

    Delphi51

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    Me, too. Another thing; the bullet from a gun is of lower speed than something that can go into an orbit, so its trajectory will be a parabola in contrast to the circle or ellipse of the orbiting cannonball.
     
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