When does the object strike the ground?

Question

An object is launched from a platform. The objects height above ground in meters, h(x), depends on time, x, in seconds after launch and can be modeled by the functions h(x)=-4.9x^2 + 20.6x + 60.8

when does the object strike the ground?

Answer 1

The maximum (half way) occurs at x = -b / 2a.

In this case x = -20.6 / 2(-4.9), or x = 2.102040816

The object then hits the ground 2.102040816 seconds later at 4.204081633 seconds

Answer 2

It strikes the ground when

h(x) = 0

Solve the quadratic equation

-4.9x² + 20.6x + 60.8 = 0

a = -4.9

b = 20.6

c = 60.8

x = [-b ± √(b² - 4ac)] / (2a)

Plug in the numbers and get x in seconds. You will get two solutions: one positive, the other negative. Since time must be positive, discard the negative solution. The positive solution is your answer.