The vertical motion of a ball falling under the influence of gravity is primarily dependent on two factors: the initial conditions of the ball and the force of gravity acting on it.
Initial Conditions: The initial conditions include the ball's initial position, initial velocity, and initial acceleration (if any). These parameters determine the starting point and behavior of the ball's motion. For example, if the ball is initially at rest, it will start from rest and accelerate downward due to gravity. If the ball has an initial upward velocity, it will eventually slow down, reverse direction, and accelerate downward until it reaches the ground.
Force of Gravity: The force of gravity is the main driving force behind the vertical motion of the ball. On Earth, the force of gravity pulls objects downward towards the center of the planet. This force is constant near the surface of the Earth and is typically denoted as 9.8 m/s². The acceleration due to gravity determines the rate at which the ball's velocity changes as it falls. As the ball falls, it accelerates under the influence of gravity until it reaches a terminal velocity (if there is air resistance) or until it hits the ground.
It's important to note that in the absence of other forces (such as air resistance), the vertical motion of the ball is independent of its mass. This is known as the equivalence principle, which states that all objects, regardless of their mass, fall at the same rate in a vacuum. However, in the presence of air resistance, the mass and shape of the ball can affect the specifics of its motion.