1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Education Advisor
    2016 Award

    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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor
    Homework Helper

    It's ok, threads are often moved to the correct place after awhile. Just wanted to draw your attention to this :-)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?