Projectiles follow an arch, which is technically a parabola when there is no air resistance.
The key to understanding this motion is to realize there are two motions simultaneously: constant horizontal velocity, and constant vertical acceleration due to gravity. And when two things are perpendicular to each other, they are also independent of each other. Sideways motion could care less about what happens vertically, and vice versa!
Check out this video, which goes through two related projectile problems, and how to set them up.
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