Algebra 2 IMPORTANT

Question

Rick launches a rocket from ground level with an initial velocity of 192 feet per second. The height of the projectile h, in fee, as a fiction of time, in seconds, is given by the following function. (Show all work)

h(t)=-16t^2+ 192t

After how many seconds is the projectile at 512 feet above ground level? Show your work.

Answer 1

If the height is 512 feet and h(t) is the height then:

512 = -16t² + 192t

16t² - 192t + 512 = 0

t² - 12t + 32 = 0

(t - 8)(t - 4) = 0

t = 8 and t = 4

The first time the projectile is 512 feet is at t = 4 seconds. Then it continues up to its maximum height then begins to fall and passes h = 512 feet again at t = 8 seconds