# Trajectory of projectile with considerable drag

1. Aug 14, 2014

### HP007

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. Aug 15, 2014

### Simon Bridge

(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 [Broken]

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.

Last edited by a moderator: May 6, 2017
3. Aug 15, 2014

### Staff: Mentor

4. Aug 15, 2014