Trajectory of projectile with considerable drag

  1. Facing some horrible mathematical situation while solving to find equation of trajectory of projectile when drag is proportional to v^2.
    my equations where i end up with are as follow:
    equation 1:
    mdv/dt=(-kv^2)+(-mgsinγ);
    equation 2:
    (-mv)dγ/dt=mgcosγ;
    equation 3:
    dx/dt=vcosγ;
    equation 4:
    dy/dt=vsiny;
    where:
    v is velocity of particle at instance when it makes an angle γ with horizontal plane.
    Initial condition is known and assume it to be u at an angle α.
    please assist me in solving this.
     
  2. jcsd
  3. Simon Bridge

    Simon Bridge 15,259
    Science Advisor
    Homework Helper
    Gold Member

    (1) ##m\dot v = -kv^2-mg\sin\gamma##
    (2) ##-mv\dot \gamma = mg\cos\gamma##
    (3) ## \dot x = v\cos\gamma##
    (4) ## \dot y = v\sin\gamma##

    Whence ##v(0)=u## and ##\gamma(0)=\alpha##

    Do you want the trajectory: (x(t),y(t))?

    Have you ever tried to solve systems of differential equations before?
    (i.e. what is the level of education help should be aimed at?)

    Have you seen:
    http://users.df.uba.ar/sgil/physics_paper_doc/papers_phys/mechan/air0.pdf

    You seem to be trying to use cartesian and some sort of polar coordinates at the same time - it is best practice to pick just one coordinate system and stick to it.
     
  4. Nugatory

    Staff: Mentor

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