First we want to calculate at what height and at what time rocket stops ascending.
h' = 256 - 32t = 0
32t = 256
t = 8
h = 256*8 - 16*8^2
h = 1024
Now we want to find time at which it gets 200 feet that means our equation is:
200 = 256t - 16*t^2
-16*t^2 + 256t - 200 = 0
t1 = 0.82s
t2 = 15.17s
time t1 is when rocket is ascending and t2 when it is descending therefore answer is t2