Question

A catapult launches a boulder with an upward velocity of 112 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h= -16t^2 + 112t + 30 .
How long does it take the boulder to reach its maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary.



A. 7 s; 30 ft
B. 3.5 s; 366 ft
C. 3.5 s; 618 ft
D. 3.5 s; 226 ft

Answer 1

To determine the time it takes for the maximum height to be achieved, derive the  equation and equate to zero. 
                        h = -16t² + 112t + 30
                       dh / dt = 0 = 2(-16)t + 112
The value of t is 3.5 s. Substitute this value of time to the equation for h,
                         h = -16 x (3.5 s)² + 112 x 3.5 s + 30 = 226 ft
Thus, the answer is letter D.