Answer: The practical domain of a mathematical model represents the set of values for which the model is applicable or makes sense in the real world. In this case, the practical domain of the ball's height model h=-16t^2+64t is limited by the physical constraints of the situation.
Since the ball is kicked upward, the height of the ball cannot be negative. Therefore, the practical domain for the height model is restricted to values of t that result in non-negative heights.
We can find the values of t that correspond to when the ball is on the ground by setting h=0 and solving for t:
0 = -16t^2 + 64t
0 = t(-16t + 64)
t = 0 or t = 4
The ball is on the ground at the start of the motion (t=0) and again after 4 seconds. Therefore, the practical domain for the height model is 0 ≤ t ≤ 4, since the ball is in the air during this time and the height model is applicable.
In summary, the practical domain of the height model h=-16t^2+64t is 0 ≤ t ≤ 4.