Height of an object t seconds after it is launched is modeled by the function h(t) = -5t^2 + 30t + 200. the object will hit the ground in how many seconds.

10 seconds

Step-by-step explanation:

When the object hits the ground, the height (y-value) is 0.

h(t) = -5t² + 30t + 200

  0 = -5t² + 30t + 200   set height equal to zero

  0 = -5(t² - 6t - 40)      factored out -5

  0 = -5(t - 10)(t + 4)     factored the quadratic

0 = t - 10     0 = t + 4    applied the Zero Product Property

  t = 10         t = -4        solved for t

                        ↓

                    t = -4 is not valid (since time cannot be negative)

So, t = 10