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Free fall describes the motion of an object exclusively under the influence of gravity. When objects free fall in physics, air resistance is often ignored, simplifying calculations. Here, the balls are said to fall from rest (starting velocity is zero), so the only force acting on them is gravity.
The principle simplifies decision-making and calculations in physics by focusing solely on the gravitational acceleration, which remains constant for objects near Earth's surface. This simplification helps in using the kinematic equations effectively to solve real-world problems like our current exercise.

The acceleration due to gravity, denoted by the symbol \( g \), is a constant value on the surface of the Earth. In our calculations, it is approximately 9.8 m/s². This value represents how quickly any free-falling object will speed up as it continues to fall.
In physics problems involving free fall, \( g = 9.8 ext{ m/s}^2 \) is typically used. This consistently helps in predicting how long it will take for objects to fall a certain distance and how fast they will be going at any point.
Because \( g \) is uniform, once you determine it, you can apply it to objects in free fall to model their movement predictably, making it a key component of kinematic equations.

The time of flight is the duration an object spends in motion from the moment it begins its fall to when it reaches a specified point. Using kinematic equations, you can find this value by solving for time, \( t \).
For this exercise, once we know the distance (3 meters in the case of the lower ball), we use the rearranged kinematic equation: \( s = \frac{1}{2} g t^2\). Solving for \( t \) yields the time it takes for the ball to fall that distance.
The second ball's time of flight starts 0.5 seconds after the first ball, affecting its position relative to the first ball, which is critical in determining the vertical separation between the two.

Displacement is a vector quantity that refers to the change in position of an object. It can be determined using the kinematic formula, which, for an object in free fall from rest, is: \( s = \frac{1}{2} g t^2\).
In this problem, to find the distance each ball has fallen, we plug the time values we calculated into this equation. For example, at 0.78 seconds, the first ball has fallen 3 meters. The second ball, starting its journey 0.5 seconds later, falls a shorter distance, calculated to be approximately 0.384 meters after 0.28 seconds.
The vertical separation, \( h \), between the two balls is simply the difference in their displacements. Knowing how to set up and solve these equations helps analyze motion accurately in physics.