Final answer:
The path of a projectile in the absence of air resistance is a parabolic shape due to constant acceleration in the vertical direction from gravity and no acceleration in the horizontal direction.
Step-by-step explanation:
In the absence of air resistance, the path of a projectile is parabolic. This is due to the constant acceleration in the vertical (y) direction due to gravity, while the horizontal (x) velocity remains constant because there are no forces acting in the horizontal direction (assuming no air resistance). When a projectile is launched, only its vertical motion is affected by acceleration due to gravity which gives the trajectory a curved parabolic shape.
For example, if a negatively charged massive particle is dropped between two plates, assuming no other forces except for gravity, it would take a rightward or leftward-curving parabolic path, depending on the initial conditions, but in a vacuum and in the absence of electrical or magnetic fields, the path simplifies to solely a parabolic trajectory.
The constant, non-zero acceleration that a projectile experiences, ignoring air resistance, is always in the y direction (vertical direction). This influence of gravity is what shapes the projectile's path into a parabola.