My Math Forum calculations invloving drag

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 November 17th, 2014, 01:45 PM #1 Senior Member   Joined: May 2012 Posts: 203 Thanks: 5 calculations invloving drag how are calculations that include the force of drag on projectile motion generally done/? the force of drag depends on the velocity of the object, which makes sense, and according to Wikipedia it depends on the square of the velocity... but now setting up a simple formula for velocity is not obvious since the force of drag, which affects the velocity, is itself dependent on the square of the velocity....
November 17th, 2014, 04:27 PM   #2
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Quote:
 Originally Posted by Kinroh how are calculations that include the force of drag on projectile motion generally done/? the force of drag depends on the velocity of the object, which makes sense, and according to Wikipedia it depends on the square of the velocity... but now setting up a simple formula for velocity is not obvious since the force of drag, which affects the velocity, is itself dependent on the square of the velocity....
Actually drag forces can be proportional to the velocity or proportional to the square of the velocity. It depends on which circumstance you are using. The motion equation then becomes, ala Newton's 2nd:
$\displaystyle \sum F = ma - (drag) = m \frac{dv}{dt} - kv^2 = 0$

-Dan

 January 9th, 2015, 12:04 PM #3 Senior Member   Joined: May 2012 Posts: 203 Thanks: 5 ok, so for a projectile assuming its launched from ground.... and assuming the simpler case where it is not the square of the velocity I have: ma=-mg-kv in the y component so I get dv/dt= -g-(k/m)v... I attempted to solve this first ;order linear d/e, using an algorithm to found online, so correct me if wrong: y component of v= -(m/k)g +ce^((-km)(t)) and I could solve for c using an initial velocity of my choice. for the x component, its simply: ma=-kv, dv/dt=-(k/m)v so solving for the x component: v= ce^(-k/m)t again solving for c with a initial velocity of my choice... Now how do I solve the d/e with the exponential assumption? I think the x component is easy: ma=-kv^2, dv/dt= -k/m(v^2) v=m(1+c)/kt... but for the y component...how do you solve an exponential fit order d/e?
 January 9th, 2015, 06:42 PM #4 Newbie   Joined: Dec 2014 From: Sioux Falls, SD Posts: 7 Thanks: 0 Drag Equations Here is a link. Im working on the same thing Flight Equations with Drag

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