A kitchen tap fills a $2.0\ \text{litre}$ jug in $12.5\ \text{s}$. The water leaves the round mouth of the tap, of area $1.6\ \text{cm}^2$, and falls straight down as a smooth stream. Ignore air resistance and surface tension, and take $g = 10\ \text{m/s}^2$. How far below the mouth of the tap is the cross-section of the stream one third of the area of the mouth? Give the answer in $\text{cm}$.