The time it takes for the boulder to reach maximum height can be determined by taking the derivative of the function and equating it to zero as in: h' = -32t + 120 = 0. This is because at the maximum point, the slope (derivative) is zero. Thus, the time it takes for the boulder to reach maximum height is 4/15 seconds or ~0.27 seconds.
To solve for the maximum height, substitute the time it takes to reach the maximum height in the given function as in: h = -16(0.27)^2 + 120(0.27) + 10. Thus, the boulder's maximum height is 41.23 ft.
