If an object is dropped from a height of 144 feet, the function h(t)=-16t^2 +144 gives the height of the object after t seconds. when will the object hit the ground?

If the object hit the ground, then this mean that the height is 0, right?
so solve for it like this: 

0= -16t^2+144
-144 = -16t^2
Divide by (-16)
9= t^2 
square root both sides
t= 3 or -3
there is no negative time then the object will hit the ground after 3 secs

When the object hits the ground, its height will be 0. So, if h(t) is the height, which it is, substitute it with 0. So:
0 = -16t^2 + 144

Now it's a quadratic function, so we factor!
0 = -t^2 + 9
0 = t^2 - 9
0 = (t+3)(t-3)
t= 3, -3
And since this is the real world, we won't worry about the negative answer. So, the object hit the ground after 3 seconds.
Hope this helps!