A model rocket is launched with an initial velocity of 164ft/sec. It's height h, in feet, after t seconds is given by the formula h=164t-16t^2. After how many seconds will the rocket first reach a height of 400ft?

Answer 1

well! , just set
164t - 16t^2 = 400

-16t^2 + 164t - 400 = 0
4t^2 - 41t + 100 = 0
(t-16)(4t - 10) = 0
t = 10 or t = 10/4 or 2.5 seconds

So it will reach that height first at 2.5 seconds,
(and again after 10 seconds on its way back down)

Answer 2

h = 164t - 16t^2 = 400 Ft.
-16t^2 + 164t = 400
-16t^2 + 164 - 400 = 0
Use Quadratic Formula and get:
t = 4, and 6.25 seconds.

Answer = 4 s. The rocket is falling when
t = 6.25 s.