Final answer:
The practical domain refers to the range of values that the variable t can take in the given mathematical model. Since the ball is kicked upward and will eventually fall back down, the domain of t is limited to non-negative values and the time it takes for the ball to reach its highest point and fall back to the ground. The practical domain in this situation is 0 ≤ t ≤ 14.
Step-by-step explanation:
The practical domain in this situation refers to the range of values that the variable t can take in the given mathematical model.
Since time cannot be negative in this context, the domain of t is limited to non-negative values. And since the ball is kicked upward and will eventually fall back down, we can further limit the domain to the time it takes for the ball to reach its highest point and fall back to the ground.
Calculating the time it takes for the ball to reach its highest point:
- Set the equation for height, h = -16t² + 56t, equal to zero to find the time at which the ball reaches its highest point.
- Use the quadratic formula to solve for t.
- The values for t will indicate the time it takes for the ball to reach its highest point and fall back to the ground, giving us the practical domain.
The correct answer is b) 0 ≤ t ≤ 14.