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 .

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. h=-16t^2+112t+30
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 boulder to reach its maximum height, derive the equation and equate to zero.
h = -16t² + 112t + 30
dh / dt = 0 = -32t + 112
The value of t from the equation above is 3.5 s. Substitute this value of t to the original question,
h = -16(3.5 s)² + 112(3.5 s) + 30 = 226 ft
Thus, the answer is letter D.