Which statement about projectile motion is true?

In projectile motion, the horizontal and vertical motions are indeed independent of each other. This independence is a fundamental principle of kinematics. When an object is projected, the horizontal motion occurs at a constant velocity (assuming air resistance is negligible) while the vertical motion is influenced by gravity, resulting in a uniform acceleration downwards.

At any given time during the projectile's flight, the horizontal displacement can be calculated using the horizontal speed multiplied by time, while the vertical displacement is influenced by the initial vertical velocity and the acceleration due to gravity. This separation of motions allows one to analyze them individually using different equations of motion, which is crucial for solving problems related to projectile trajectories.

The other statements do not hold true in the context of projectile motion. The vertical motion is indeed affected by gravity, which causes an acceleration downwards. The horizontal motion does not vary with time; it remains constant in ideal conditions. Lastly, the maximum height of projectiles varies based on their initial velocity and launch angle; not all projectiles will reach the same height. Only when launched under identical conditions will they have the same maximum height.