A stone projected vertically upward on some planet reaches a maximum height $$h$$. Find the ratio of times (earlier to later, as a decimal) after projection when it is at a height of $$\frac{5h}{9}$$.

Let $$T$$ be the time to reach the top, so $$u = gT$$ and $$h = \frac{gT^2}{2}$$. At height $$\frac{5h}{9}$$, $$gTt - \frac{gt^2}{2} = \frac{5}{9} \cdot \frac{gT^2}{2}$$, i.e. $$t^2 - 2Tt + \frac{5}{9}T^2 = 0$$. Then $$t = T\left(1 \pm \frac{2}{3}\right)$$, i.e. $$\frac{T}{3}$$ and $$\frac{5T}{3}$$, and the ratio is $$1 \colon 5 = 0.2$$.