Question

11. A rocket is fired upward from some initial height above the ground. Its height h in feet above the ground t seconds after it is fired is given by h = -16t2 + 48t +448.
(i) What is its initial height? __________ ft.
(ii) What is its maximum height? ___________ ft.
(iii) How long does it take to reach the ground? __________ sec.

Answer 1

initial height is when t=0. 448

h = -16(t² - 3t - 28)
= -16(t-7)(t+4)

Note that h=0 when t=7. That's the answer to part iii

Since the two roots are -4 & 7, the apex is reached at t = (-4 + 7)/2 = 1.5

h(1.5) = -16(5.5)(5.5) = 484 ft

Answer 2

-16t^2+48t+864