I need to write down a model for a man parachuting from a plane at a height $h$ above the ground, having a velocity $v_{\text{plane}}$. I've had a look at many models online and they all start saying that $F=ma=-kv-mg$. Where $k$ is the air resistance before the deployment of the parachute, $v$ is the velocity, $m$ is the mass of the man and $g$ is the acceleration. However, I think that the trajectory should also be in three dimensions, i.e. $F=(F_x,F_y,F_z)$, cause with the jump from the plane, the man should have an initial velocity coming from leaning out of the plane, and therefore there should also be some air resistance in that direction.
Is that correct or can we neglect it?
Furthermore, I don't understand why $ma=-kv-mg$, I mean this two forces should oppose eachother shouldn't they? The air resistance should be in the opposite direction compared to the acceleration due to the gravity. I really hope you can help me with this!