Probability — practice question

A particle $P$ with mass $0.2\,\text{kg}$ is fastened to one end of a light elastic string whose natural length is $1.6\,\text{m}$ and modulus of elasticity is $18\,\text{N}$. The opposite end of the string is fixed at point $O$, which lies $1.6\,\text{m}$ vertically above a smooth horizontal surface. $P$ is placed on the surface directly below $O$ and then projected horizontally. $P$ travels in a straight line along the surface with initial speed $1.5\,\text{m s}^{-1}$. Show that, when $OP = 1.8\,\text{m}$,