Resolving projectile motion into perpendicular directions works because each direction can then be treated as:

1. The point of resolving is to reuse machinery already built. 2. The key to analyzing projectile motion is to resolve it into motions along perpendicular directions. 3. The horizontal and vertical components are independent of each other. 4. Each component is therefore a straight-line problem of the kind one-dimensional kinematics already solves. 5. Recombining them gives back the curved path. _Source: OpenStax College Physics for AP(R) Courses 2e (CC BY 4.0), Ch 3 'Two-Dimensional Kinematics', sections 3.1-3.4_