I'm stuck in the following question: One end of a light inextensible string of length $a$ is attacheded to a fixed point $A$, a distance $\frac{13a}{27}$ below a horizontal ceiling. The other end supports a particle which is projected from its lowest point with a horizontal speed $\sqrt{\lambda g a}$. Find the smallest value of $\lambda$ for which the particle will reach the ceiling before the string goes slack.
At the lowest point, I'm assuming the particle has kinetic energy $\frac{1}{2}m\lambda g a$ and potential energy of $0$. I'm not sure what to do next.