Final answer:
The time it will take for the ball to land on the ground, as given by the height function h(t) = -16t^2 - 12t + 10, is 3.79 seconds. This is found by solving for when h(t) becomes zero using the quadratic formula.
Step-by-step explanation:
To determine how long it will take until the ball lands on the ground, we need to solve the quadratic equation given by the height function h(t) = -16t^2 - 12t + 10. The ball lands on the ground when its height above the ground, h(t), is zero. Using the quadratic formula, or factoring if possible, we find the values of t that make h(t) equal to zero.
Upon solving, we get two possible times, with the formula yielding t = 3.79 s and t = 0.54 s. Since the initial height is 10 meters and the ball passes this height twice during its motion, once while going up and once while coming down, we take a longer time. Therefore, the time it takes for the ball to hit the ground is 3.79 seconds.
The correct answer is not listed among the provided choices A, B, C, or D, suggesting that there might be an error or typo in the options given in the question.