Acatapult launches a boulder with an upward velocity of 120 ft/s. the height of the boulder, h, in feet after t seconds is given by the function h = -16t^2 + 120t + 10. how long does it take to reach maximum height? what is the boulder's maximum height? what is the boulder's maximum height? round to the nearest hundredth, if necessary.

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.