Final answer:
In projectile motion, the range or horizontal distance is mainly influenced by the initial horizontal velocity, the angle of launch, and air resistance. The horizontal and vertical motions are independent, and the horizontal distance depends on how long the projectile is in the air, which is a result of the vertical motion components.
Step-by-step explanation:
In projectile motion, the horizontal distance traveled by a projectile, known as the range, is affected by several factors. The main factors are the initial velocity of the projectile in the horizontal direction, the angle of launch, and the effects of air resistance, although this last factor is often negligible in basic physics problems. The horizontal motion of a projectile is independent of its vertical motion; this means that the horizontal velocity remains constant (assuming no air resistance), and the horizontal distance covered depends directly on the time the projectile spends in the air, which is determined by its initial vertical velocity and the acceleration due to gravity.
The range equation for projectile motion is valid only when the projectile lands at the same elevation from which it was launched. Therefore, in cases like a bullet shot horizontally from shoulder height, the timing of when the bullet hits the ground, along with its initial speed, can be used to determine how far it will travel horizontally before it lands.