Which factor correlates with the horizontal range of a projectile?

The horizontal range of a projectile is influenced by several factors, making the option that encompasses all of them the most accurate choice.

The height of the gun's position affects the range because launching a projectile from a higher elevation allows it to travel a greater distance before hitting the ground. This is due to the increased initial potential energy and the longer time it remains in the air.

The speed of the projectile is a critical factor as well; a higher launch speed translates to greater initial kinetic energy, allowing the projectile to cover more ground before gravity and air resistance bring it down. The speed directly impacts how far the projectile can travel horizontally.

Additionally, the angle of the projectile's departure is fundamental. Launching a projectile at the optimal angle (45 degrees in a vacuum, assuming no air resistance) maximizes its range. Angles above or below this optimum result in lower horizontal distances.

Since all of these factors - the height of the gun's position, the speed of the projectile, and the angle of departure - contribute to the horizontal range, selecting the option that includes all of them encompasses the complete understanding of the variables at play in projectile motion.