Probability — practice question

A light elastic string has a natural length of $2.4\,\mathrm{m}$ and an elasticity modulus of $21\,\mathrm{N}$. A particle $P$, with mass $m\,\mathrm{kg}$, is fixed to the midpoint of the string. The two ends of the string are fastened to fixed points $A$ and $B$, which are $2.4\,\mathrm{m}$ apart and lie at the same horizontal height. $P$ is projected vertically upward from the midpoint of $AB$ with speed $12\,\mathrm{m\,s^{-1}}$. In the ensuing motion, $P$ is momentarily at rest at a point $1.6\,\mathrm{m}$ above $AB$.