14400=1600t-16t^2 is the equation of vertical motion for a body acted on by gravity (32 ft per sec per sec is the acceleration of gravity). So 16t^2-1600t+14400=0=t^2-100t+900=(t-10)(t-90). So t=10 or 90 seconds. The larger value applies if the rocket falls back to earth because its boosters don't operate. (In actual fact the pull of gravity decreases as the rocket penetrates the atmosphere at higher levels. The equation of motion assumes the gravitational acceleration is constant.) The answer is therefore 10 seconds: 1600*10-16*100=16000-1600=14400 feet.