I came across this problem from the Cambridge Ex 2 book, the Mechanics section.
Part (d) has me scratching my head. Obviously \alpha cannot be 1. This results in an improper integral.
From part (c)
\begin{align*}
\dot{y}^2 &= \frac{3g(3 - 2y)}{3 + 2y} \,\,\, \text{which simplifies to }...