Final answer:
To find the height of the coaster at different times, use synthetic division and substitute the values of t into the equation h(t) = 16t - 1.5(t² - 5t) - 58.75.
Step-by-step explanation:
To find the height of the coaster at different times, we need to use synthetic division.
Given the quadratic equation t² + t - 20 = 0, the roots of the equation are t = -5 s and t = 4 s. Since the ball is released at t = 0, we discard the negative root.
Therefore, the height of the coaster at t = 8 s, 9 s, 10 s, and 11 s can be found by substituting the corresponding values of t in the equation h(t) = 16t - 1.5(t² - 5t) - 58.75.