Alexis, once the rocket has reached the top of its flight, it is simply a falling body. We can use the falling body equations to learn the relationship between time and height.
let h(t) be the height of the rocket t seconds after it reached the top. So h(0) = 96.
The formula is h(t) = 96 -1/2 at2, where a = 32 ft/Sec/Sec
We want to find the t that makes h = 0
t2 = -(h-96)/16 where h = 0
t = sqrt( 96/16 )
Finish the calculation, and you’ll have the number of seconds after the rocket reached its peak.
NOTE: the other answers to this question all come up with 7 seconds from launch or 4 seconds from the apex. Here’s why I disagree:
This is partly a physics question and partly a math question. A rocket has fuel which it burns up as it goes up, so it has a varying acceleration and, since it consumes the fuel, it has a varying mass. As a result, its flight upward is not a parabola. We don’t know its complicated formula. But... we don’t need to!
Once it has reached its apex and run out of fuel, it is simply a falling object, and its behavior follows the quadratic function given above, and the answer is
sqrt(96/16) = sqrt(6) after reaching the apex, or
3+ sqrt(6) after launch.