Aprojectile is launched straight up with an initial velocity of 120 ft/s. if acceleration due to gravity is -16ft/s^2 after about how many seconds will the object reach a height of 200ft

The object will raise the height of 200 feet after 2.5 s. Taking as origin zero coordinates when the object is launched. You can see the solution in the attached document.Note: the second root found (5 s) has no physical effect for this particular problem, therefore, it is discarded.