I wanted to look at the behaviour of an airplane as it lifts off at an angle, while considering air resistance. So basically if I'm not mistaken, the simple definition of it is that it's the force acting opposite to the instantaneous direction of motion and for large things it's directly proportional to v^2.
I'm wondering if anyone can help me to set up the starting differential equation for it.
My basic idea is to start with the net force equation: Fnet=F applied - F drag, so the differential equation would look something like dv/dt = a - kv^2 where k is a constant and a is the constant acceleration of the plane. However, I'm not sure how to integrate the fact that the force is going to be at an angle (like 45 degrees from the horizontal) and incorporate both vertical and horizontal components?
Any help is appreciated!
I'm wondering if anyone can help me to set up the starting differential equation for it.
My basic idea is to start with the net force equation: Fnet=F applied - F drag, so the differential equation would look something like dv/dt = a - kv^2 where k is a constant and a is the constant acceleration of the plane. However, I'm not sure how to integrate the fact that the force is going to be at an angle (like 45 degrees from the horizontal) and incorporate both vertical and horizontal components?
Any help is appreciated!
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