Projectile Motion in Polar Coordinates

This is a twist on a first year physics problem of modeling the position of a projectile. As a Graduate Teaching Assistant (GTA) we end up marking the same or similar questions on quizzes a lot! So to try something different, I decided to retry this problem which I first considered early as an undergraduate. Although it isn't a particularly hard problem, it was new and somewhat interesting to try again! It can be found embedded below.

You can also download it here.