Final answer:
To find when the golf ball is 44 feet in the air, we set the height formula equal to 44 and simplify the quadratic equation to 4t² - 24t + 11 = 0. The quadratic formula yields two positive times, t = 3.79 s and t = 0.54 s, with the former likely representing the time on the way down.
Step-by-step explanation:
To find at what times the golf ball is 44 feet in the air, we start with the given equation for the height of the golf ball h = 96t - 16t² and set it equal to 44, which gives us 96t - 16t² = 44. Next, we rearrange the equation to get a quadratic equation in standard form, resulting in -16t² + 96t - 44 = 0. To simplify the equation, we can divide through by -4 to obtain 4t² - 24t + 11 = 0. Factoring such a quadratic equation directly can be challenging and might not always be possible. Therefore, in cases where factoring is complicated or not feasible, we would typically use the quadratic formula to find the solutions for t. It's important to remember that we are looking for positive times, as negative times would not make physical sense in this context.
Since the provided information mentions using quadratic formula giving times t = 3.79 s and t = 0.54 s, these would be the times at which the ball is at a height of 44 feet; once when the ball is on its way upwards, and once on its way downwards. The longer of these two times, 3.79 seconds, represents the time it would actually take for the ball to reach the maximum height and then descend back to 44 feet on its way down.