Answer
It takes 7 seconds for the object to reach the ground.
Work Step by Step
For $h = -16t^2 + 784$, $h$ is to be measured from the ground up, and when the object reaches the ground, $h = 0$, hence,
$0 = -16t^2 + 784$
$16t^2 = 784$
$t^2 = 49$
$t = \pm 7$
So, $t = 7$ or $t = -7$ (rejected)
It takes 7 seconds for the object to reach the ground.