A rocket sets out from x $=$ x$=0$ at t $=$ t $=0$ and moves with speed u in the

negative x$-$direction, as measured in S$\text{'}.$ After $1$ year has elapsed in S$\text{'},$ the rocket

turns around. According to observers in S$,$ the rocket turns around at x $=1/5$ light year and it returns to the origin in S at x $=4$ light$-$years.

i$)$ Calculate v $/$c$.$

ii$)$ Calculate u $/$c$.$

iii$)$ At what time in S does the rocket return to the origin in S$?$