Final answer:
The maximum height of the ball is approximately 164.375 feet. It takes approximately 6.33 seconds for the ball to hit the ground.
Step-by-step explanation:
The maximum height of the ball can be found by determining the time when the ball reaches its peak height. This occurs when the velocity of the ball is zero. To find this time, we need to solve the equation -16t^2 + 108t + 28 = 0. Using the quadratic formula, we find that the time is t = 3.375 seconds. We can substitute this time back into the height function to find the maximum height, h(t), which gives us h(3.375) = -16(3.375)^2 + 108(3.375) + 28 = 164.375 feet. So, the maximum height of the ball is 164.375 feet.
The time it takes for the ball to hit the ground can be found by setting the height function equal to zero and solving for t. So, we have -16t^2 + 108t + 28 = 0. Again, we can use the quadratic formula to find that the two solutions are t = 0.171875 seconds and t = 6.328125 seconds. Since the ball was thrown from a height of 28 feet, we are only interested in the positive solution, which is t = 6.328125 seconds. Therefore, it takes approximately 6.33 seconds for the ball to hit the ground.