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Why do projectiles follow curved paths?

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A diagram with labeled vector illustrations. Panel A shows vector addition with two green arrows A and B forming a parallelogram, and their sum C as a red diagonal. Panel B shows vector subtraction, with A and negative B forming resultant D. Panel C demonstrates vector components using angles and projections. Panel D uses the right-hand rule with thumbs to show the direction of the cross product E = A x B and its opposite, -E = B x A. — mechanics Figure 1: (A) The vector sum C = A + B = B + A. (B) The vector difference A + (−B) = A − B = D. (C, left) A cos θ is the component of A along B and (right) B cos θ is the component of B along A. (D, left) The right-hand rule used to find the direction of E = A × B and (right) the right-hand rule used to find the direction of −E = B × A.

Projectiles follow curved paths because their motion is the result of two independent components: constant horizontal motion and vertical motion influenced by gravity.1

According to the principles of mechanics, a projectile launched into the air maintains a constant horizontal velocity, as described by the law of inertia. Simultaneously, the object is subject to a constant downward acceleration due to gravity, which causes it to fall vertically. The combination of these two motions—moving forward at a steady rate while accelerating downward—creates a parabolic trajectory.12

While this idealized model assumes the absence of other forces, actual flight paths are often modified by air resistance (drag), which retards motion, and other factors such as wind or the rotation of the Earth. In the absence of these external influences, the parabolic shape remains a fundamental characteristic of projectile motion.12