Answer
The center of mass is 25.1 cm from the bottom of the handle. This point will follow a parabolic trajectory.
Work Step by Step
Let $x=0$ be the bottom of the handle. By symmetry, the center of mass of the 2.30-kg cylinder is located at the center of the cylinder which is a distance of 28.0 cm from the bottom of the handle. The center of mass of the 0.500-kg handle is a distance of 12.0 cm from the bottom of the handle.
$x_{CM} = \frac{(2.30~kg)(28.0~cm)+(0.500~kg)(12.0~cm)}{2.30~kg + 0.500~kg}$
$x_{CM} = 25.1~cm$
The center of mass is 25.1 cm from the bottom of the handle. This point will follow a parabolic trajectory.
