# Physics: Motion of an Object With Linear Drag

If you throw a tennis ball at normal human speeds, you can model this as projectile motion. For projectile motion, the object has a constant horizontal velocity and a vertical acceleration of -g (where g = 9.8 N/kg). However, if you crumple up a piece of paper and throw it something different happens. In this case we have to also include the interaction between the air and the paper to properly model the motion of the object.

When an object moves through some medium, things can get really complicated. Not only does each little particle of the medium (fluid or air) bounce off the object, but you can get weird effects from the fluid moving around the back of the object also.

In the end, we just need a model for the drag force on a moving object. The two most common models are linear and quadratic drag.

In the linear drag model, the force from the fluid is backwards pushing and proportional to the velocity. For quadratic drag, it’s proportional to the square of the magnitude of velocity. Here, I’m only going to consider linear drag. This model is most appropriate for things moving through thicker fluids or for very tiny objects in the air. It’s also…