Final answer:
The sunglasses will hit the ground after 3 seconds.
Step-by-step explanation:
The equation h(t) = -16t² + 2304 represents the height of an object thrown upward. In this case, it represents the height of sunglasses. To find when the sunglasses hit the ground, we need to find the value of t when h(t) is equal to zero. We can set the equation -16t² + 2304 = 0 and solve for t using the quadratic formula.
Using the quadratic formula, we have t = (-b ± sqrt(b² - 4ac)) / (2a), where a = -16, b = 0, and c = 2304. Plugging these values into the formula, we get t = (-0 ± sqrt(0 - 4*(-16)*2304)) / (2*(-16)). Simplifying further, we have t = sqrt(4*2304) / 32, which gives us t = sqrt(9216) / 32. Taking the positive square root of 9216, we get t = 96 / 32 = 3 seconds.
Therefore, the sunglasses will hit the ground after 3 seconds.