$7\mathrm{.}4\mathrm{.}23.[$Level $2]$ A freely hinged bar $($initially stationary$)$ is impacted by a mass particle A moving with velocity $v{b}_1.$ Let the mass of the bar be $m$ and the mass of the particle be $m.$ Assume a coefficient of restitution equal to $0\mathrm{.}5$ and determine the velocity of the mass particle immediately following the collision.