The key to projectile motion is the idea that the vertical motion and the horizontal motion are essentially independent of each other. You can try a very simple (and fun) experiment.

Season 2 Episode 405 | 30m 1s Projectile Motion: The terms projectile and trajectory are introduced. Students learn to describe horizontal and vertical components of a projectile’s motion.

That's exactly the same as projectile motion in your introductory physics course. The key to this kind of motion is that the horizontal and vertical motion of the ball can be treated independently.