At $12.5$ seconds after launch.
Work Step by Step
We know that the polynomial $-16t^2+200t$ gives the height of the rocket at any time $t$. To find the moment at which the rocket hits the ground, we resolve for $t$ : $$-16t^2+200t=0$$ We have $t(-16t+200)=0$ by factorizing which means the rocket hits the ground for $t$ such that $-16t+200=0$. We get $200=16t$ and by dividing $t=200/16=12.5$ The answer is thus at $12.5$ seconds.