H= -16t^2+16t+192 When will the ball hit the ground?

t = 4 s

Step-by-step explanation

We can infer the origin from the t⁰ term of the quadratic as being 192 feet above the ground. Initial velocity is  16 ft/s from the t¹ term, gravity is -32 ft/s² from the t² term

0 = -16t² + 16t + 192

0 = -t² + t + 12

0 = t² - t - 12

0 = (t - 4)(t + 3)

so either

t - 4 = 0

t = 4 s

or

t + 3 = 0

t = -3 s  which we ignore as it occurs before the ball is released.