Problem $3\mathrm{.}1348$

A disk A with mass $m$ moves on a frictionless horizontal surface. The disk is attached to point $O$ with an elastic cord. The disk follows the trajectory shown between $(1)$ and $(2).$ The coordinates of $A$ at $(1)$ and $(2)$ are $(x_1,y_1)=(-1\mathrm{.}5,5\mathrm{.}0)cm$ and $(x_2,y_2)=(4\mathrm{.}0,-3\mathrm{.}0)cm,$ respectively. If the velocity of $A$ at $(1)$ is parallel to the $y$ axis and has a magnitude $v_1=2\mathrm{.}0\frac{m}{s},$ determine $v_2,$ the speed of $A$ at $(2),$ knowing that $=35.$