Final answer:
To find the time a thrown ball takes to hit the ground, we use the quadratic formula with the given equation, resulting in two times. We select the longer time, 3.79 seconds, as it accounts for the ball's upward and downward journey.
Step-by-step explanation:
The question presented is about determining the time it takes for a thrown ball to hit the ground, using the given equation h(t) = -4.9t2 + 6t + 8, which describes the parabolic motion of the ball under Earth's gravity. To find when the ball reaches the ground, we need to solve for t when h(t) = 0. We employ the quadratic formula to determine the time at which the ball hits the ground.
Using the quadratic formula, two solutions are obtained: t = 3.79 s and t = 0.54 s. Since the question specifies that Antonio threw the ball upwards, the ball will reach a peak height before descending back to the ground. Thus, we are interested in the longer time duration it takes for the ball to hit the ground, which in this case is 3.79 seconds.