# Trajectory of projectile with considerable drag

 P: 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.
 Homework Sci Advisor HW Helper Thanks P: 13,093 (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_...echan/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.
 Mentor P: 3,956 This problem has come up before. Try this thread: http://www.physicsforums.com/showthread.php?t=712807
P: 3
Trajectory of projectile with considerable drag

 Quote by Nugatory This problem has come up before. Try this thread: http://www.physicsforums.com/showthread.php?t=712807

But I have already arrived at those set of coupled equations I want to know the way to solve it.
Assist me in solving mathematical part of the problem.

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