A putty ball of inertia \(m\) moving at speed \(v_{\mathrm{i}}\) slides on a slick horizontal surface along a path that is perpendicular to the long axis of a rod of length \(\ell\) and inertia \(2 m\) that is at rest on the surface. The ball collides with one end of the rod and sticks to it.

(a) Just as the ball sticks, where is the center of mass of the ball-rod system? After the collision, what are 

\((b)\) the magnitude and direction of the velocity of the center of mass and \((c)\) the rotational speed of the system? Ignore any effects due to friction.