# Trajectory of projectile with considerable drag

1. ### HP007

3
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. ### Simon Bridge

15,282
(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.

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