If a rocket is propelled upward from ground level, its height in meters after t seconds is given by h=-9.8t^2+88.2t. During what interval of time will the rocket be higher than137.2m?

Question

Do I set it up like this?

-9.8(1)^2+88.2(1)+137.2 = 215.6

Then h=b/2a=9.8/215.6=22m

137.2+22=159

Thanks for your help.

Answer 1

Not quite. You found (sort of) when the height is greatest (the vertex of the parabola). That was not the question.

You have

h=-9.8t^2+88.2t
when is h=137.2?

(Aside. You sure about that 9.8? h = vt - 1/2 at^2 and a = 9.8)

137.2 = -9.8t^2 + 88.2t
t = 2,7

So, at those two times, h=137.2

Knowing what you do about the shape of parabolas, and that this one opens downward, h > 137.2 between those two values, so

2 < t < 7