Final answer:
By setting the height equation h(t) to zero and solving the resultant quadratic equation using the quadratic formula, we can find the time it takes for the ball to reach the ground. Only the positive value of 't' is meaningful as the negative value implies time before the ball was thrown. We discard the negative solution and take the positive one to find the approximate time to ground.
Step-by-step explanation:
To determine the time it takes for the ball to reach the ground, we set the height function h(t) = -16t² + 648t + 100 equal to 0 and solve for 't'. This function is a quadratic equation in the form at² + bt + c = 0, where a, b, and c are constants. We can resolve this equation for 't' using the quadratic formula t = (-b ± √(b² - 4ac)) / (2a). Plugging in the values, we get:
t = (-648 ± √(648² - 4(-16)(100))) / (2(-16))
Calculating the discriminant √(648² - 4(-16)(100)) and simplifying, we will have two possible solutions for 't'. Out of the two, we discard the negative value since time cannot be negative. The positive value will give us the time when the ball hits the ground.
As we solve, we'll find that the approximate time it takes for the ball to reach the ground is closest to one of the options provided in the question.