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 give
n 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
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.
