Final answer:
The maximum height of a projectile is determined primarily by the vertical component of the initial velocity. Gravity negatively affects the trajectory, while air resistance is usually neglected for calculations.
Step-by-step explanation:
The maximum height achieved by a projectile, such as a basketball player's jump shot, depends mostly on the vertical component of the initial velocity. This principle also applies to other objects in projectile motion like rocks thrown into the air or fireworks. The acceleration due to gravity has a negative impact on the trajectory, while the initial velocity has a positive one, ultimately determining the peak altitude reached by the projectile. Air resistance can affect this, but for the sake of calculations, it is often neglected to simplify the problem.
For a basketball player to achieve a certain maximum height during a jump, the required vertical velocity can be calculated using kinematic equations, keeping in mind that the horizontal velocity (if maintained constant, as in running towards the basket) does not affect the vertical motion.