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The term that describes the path followed by a projectile in motion is "trajectory." In physics, a trajectory refers to the specific path that an object follows as it moves through space, particularly when influenced by forces such as gravity and air resistance. When a projectile is launched, its motion is determined by the initial velocity, angle of launch, and the acceleration due to gravity, all of which define its unique trajectory.

The trajectory can be visualized and often takes the shape of a parabolic curve when air resistance is negligible, which is common in introductory physics problems. This concept is fundamental in understanding projectile motion, allowing one to predict and analyze the motion of projectiles accurately.

While “arc” might seem relevant in describing a portion of the path a projectile sometimes follows, it does not encompass all projectile motions, particularly when they may not be perfect curves. "Vector" refers to quantities with both magnitude and direction, and "pathway" is a more general term that lacks the specificity required in physics to describe the motion of projectiles. Therefore, trajectory is the precise term needed to convey the concept accurately in the context of projectile motion.