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Firing a spherical bullet into a watertank

  1. Apr 30, 2008 #1
    I've got a problem, involving non-constant acceleration:

    If we fire a spherical bullet horizontally into a watertank, how far will the bullet traverse?

    I've figured as much that a spherical bullet provides a retarding force:

    [tex]F = -k \cdot v[/tex] where k is a constant.

    This should provide the following non-constant acceleration due to Newtons 2nd law.

    [tex]a = \frac{F}{m} = - {\frac{k v}{m}}[/tex]

    I'm thinking I should integrate two times over a(t) to get an expression for x(t), but since "a" is proportional to v(t) and not directly to t, I dont know how to do it without getting a recursive expression.
  2. jcsd
  3. Apr 30, 2008 #2

    Andy Resnick

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    The differential equation to solve is:

    [tex]m \ddot{x} - k \dot{x} = 0[/tex]

    And solutions are fairly straightforward to find.
  4. Apr 30, 2008 #3


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    you already posted this in HW-section.
  5. Apr 30, 2008 #4
    Yes, my apologies. I started this thread before I noticed one should ask such questions i the HW-section. I'm going to post my reply to Andy there, you may remove this thread.
  6. Apr 30, 2008 #5


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    It's ok, threads are often moved to the correct place after awhile. Just wanted to draw your attention to this :-)
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