The movement of the ball may be modeled using the equation of motion:
s = ut + 0.5at²
Where s is the distance, in this case height (h), u is the initial velocity, t is the time and a is the acceleration, in this case it is acceleration due to gravity and has a direction opposite to the velocity. We will take the downward direction to be negative, and we also know that the acceleration due to gravity is 32 feet per seconds squared. Thus:
h = 0.5(-32)t² + 30t
h = -16t² + 30t
Next, we know that the ball's initial height was 4 feet above the ground, so we add 4 to the equation to get the final equation:
h = -16t² + 30t + 4
