A stationary uniform solid sphere of mass \(M\) and radius \(R\) (with rotational inertia \(I_{\text{solid}} = \dfrac{2}{5}MR^2\)) rests on a rough horizontal surface. A cue delivers a sharp horizontal impulse \(J\) at the precise height \(h\) above the central horizontal axis where a thin spherical shell of the same mass and radius (with rotational inertia \(I_{\text{shell}} = \dfrac{2}{3}MR^2\)) would immediately roll without slipping with zero friction force during the strike. Because the sphere struck is solid, it initially slips before transitioning to pure rolling without slipping. What is the final speed \(v_f\) of the center of mass of the solid sphere once it rolls without slipping?