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Trajectory of projectile with considerable drag 
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#1
Aug1414, 11:00 PM

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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
Aug1514, 04:19 AM

Homework
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HW Helper
Thanks
P: 13,093

(1) ##m\dot v = kv^2mg\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. 


#3
Aug1514, 04:46 AM

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P: 3,956

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



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