A rocket is launched upward with a velocity of 128 feet per second from the top of a 65-foot structure. What is the maximum height attained by the rocket?

Answer 1

h = -16t^2 + 128t +65

h' = -32t +128 =0

t = 128/32 = 4 seconds to reach max height

h(4) = -16(4)^2 + 128(4) + 65

= -256 + 512 +65

= 321 feet = maximum height

or rewrite h(t) in vertex form

h = -16t^2 +128t +65

= -16(t^2 - 8t + 16) +65 + 16^2

=-16(t-4)^2 + 256+65

=-16(t-4)^2 + 321

vertex is (4,321) where the y coordinate = max height= 321 ft