The height of the object after 2 seconds will be 192 feet.
Explanation
The height after [tex]t[/tex] seconds is given by....
[tex]h= -16t^2+128t[/tex]
Now for finding the height of the object after 2 seconds, we need to plug [tex]t=2[/tex] into the above equation. So we will get.....
[tex]h=-16(2)^2 +128(2)\\ \\ h=-64+256=192[/tex]
So, the height of the object after 2 seconds will be 192 feet.