7.07 is incorrect

Your answer is partially correct. The figure is an overhead view of a thin uniform rod of length 0.555 m and mass M rotating horizontally at angular speed 14.2 rad/s about an axis through its center. A particle of mass M/3 initially attached to one end is ejected from the rod and travels along a path that is perpendicular to the rod at the instant of ejection. If the particle's speed Vp is 7.46 m/s greater than the speed of the rod end just after ejection, what is the value of Vp? Rotation axis Number 7.07 Units m/s