What determines the greatest horizontal distance a projectile can achieve?

The greatest horizontal distance a projectile can achieve is primarily determined by its horizontal velocity at launch. This is because the range or horizontal distance traveled by a projectile is influenced by how fast it moves horizontally when it is launched. A higher horizontal velocity means that the projectile will cover more distance in the same amount of time it is in the air.

To maximize the horizontal distance, the overall projectile motion can be analyzed using the equations of motion, where the horizontal motion is independent of the vertical motion. While other factors like the angle of launch also play a significant role in achieving the maximum range, it's the horizontal component of the projectile's velocity that directly dictates how far it travels along the ground before landing.

Mass does not affect the horizontal distance traveled if air resistance is negligible, and although vertical velocity is important for determining the time of flight, it is not the main factor influencing the horizontal distance directly. Thus, the greatest horizontal distance achieved by a projectile is indeed maximized by having the greatest horizontal velocity in conjunction with an optimal launch angle.