Projectile Motion with Linear Drag
With normal (plain vanilla) projectile motion, there’s only one force acting on an object — the downward pulling gravitational force. If the object is near the surface of the Earth, this force is constant. With a constant force, projectile motion is fairly (but not completely) straight forward.
But what about the motion with some type of drag force? That’s a bit more interesting. As an object moves through a medium (like a ball moving through the air), there is some type of interaction between them. It seems clear that this interaction would at least depend on the size of the object and the speed of the object.
In fact, we could model this ball-air interaction as having a term that is proportional to the velocity (linear drag) and one that depends on the square of the velocity (quadratic drag).
For some situations (low speed is one of them), the linear drag term is much more significant than the quadratic term. Let’s assume that we ONLY have linear drag so that we can model the motion of an object. For this linear drag, the coefficient (b) depends on the diameter of the object (D) and a coefficient that depends on the shape and the medium (β).
Motion in 1D
So, how would an object move with a linear drag force such as this? Yes, I’m going to do this in two dimensions but let’s…
