Final answer:
The horizontal displacement of a projectile, assuming no air friction and with acceleration due to gravity (–g), depends solely on the horizontal component of its initial velocity.
Step-by-step explanation:
The horizontal displacement of a projectile depends on the horizontal component of its initial velocity only. In analyzing projectile motion, the motions in the vertical and horizontal directions are independent of each other when air resistance is negligible. The time in the air is determined by the vertical motion, but the horizontal displacement can be calculated directly from the horizontal component of the projectile's velocity and the time in air.
According to kinematics, the horizontal acceleration (ax) is zero when air resistance is ignored, meaning the horizontal velocity (vx) is constant during the flight. This implies that the horizontal displacement depends solely on the constant horizontal velocity (vx) and the duration of the flight, which in turn is determined by the vertical component of velocity and the acceleration due to gravity (g).