Here's why:
* Gravity acts vertically: The primary force acting on falling bodies and projectiles is gravity, which pulls objects downwards. This force operates solely in the vertical dimension.
* Horizontal motion is independent: In projectile motion, the horizontal velocity remains constant (ignoring air resistance). The horizontal motion doesn't directly affect the time it takes for the object to fall.
* Vertical displacement determines time: The time it takes for an object to fall or reach a certain height is directly determined by its vertical displacement and the acceleration due to gravity.
Example:
Imagine throwing a ball horizontally from a cliff. The ball's horizontal motion is constant, but it's the vertical descent that determines how long it takes to hit the ground. The time it takes to fall is influenced by factors like the height of the cliff and the acceleration due to gravity, all of which operate within the vertical dimension.
Therefore, while projectile motion involves both horizontal and vertical components, time is primarily controlled by the vertical dimension because gravity, the dominant force, acts in that direction.
