Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Parabolic Path of a Projectile

  1. Jul 11, 2009 #1
    How do we know, or how can we prove that the path of a projectile is (at least part of) a parabola?
  2. jcsd
  3. Jul 11, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper


    In the vertical direction
    F = ma = m\frac{d^2 y}{dt^2} = -mg

    Integrated twice we obtain
    y(t) = y(0) + v_y(0)t - \frac{1}{2}gt^2

    Which is indeed the equation of a parabola with respect to time.

    Now in the x-direction, we have
    x(t) = x(0) + v_x(0)t
    since there is no force in this direction. It should be clear that if we re-write y(t) in terms of x(t), by solving for t in the above equation, y(t) will also be a parabola in terms of x.
  4. Jul 11, 2009 #3


    User Avatar
    Homework Helper

    A parabola occurs under the simplified case of a flat earth and a constant gravitational field and no aerodynamic drag. For a spherical earth, with no drag, and the equivalent of a point source for gravity, the path is part of an ellipse.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Parabolic Path of a Projectile
  1. Parabolic Motion (Replies: 12)