Arturo O. answered • 07/05/16

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First, let us edit the given height equation:

h(t) = -16t^2 + vt +c

For c = 2 ft and v = 30 ft/s,

h(t) = -16t^2 + 30t + 2

Let h = 20 ft, and solve for t.

20 = -16t^2 + 30t + 2

-16t^2 + 30t - 18 = 0

8t^2 - 15t + 9 = 0

D = discriminant = (-15)^2 - 4(8)(9) = -63

D = -63 < 0, so there is no real solution, and the object will not reach 20 ft