Answer
(a) The center of mass is 0.404 meters from the hip joint.
(b) Relative to the hip joint, the center of mass is located at the coordinates (0.317 m, -0.087 m).
Work Step by Step
(a) $x_{cm} = \frac{m_1x_1+m_2x_2}{m_1+m_2}$
$x_{cm} = \frac{(8.60~kg)(0.230~m)+(5.25~kg)(0.690~m)}{8.60~kg+5.25~kg}$
$x_{cm} = 0.404~m$
The center of mass is 0.404 meters from the hip joint.
(b) $x_{cm} = \frac{m_1x_1+m_2x_2}{m_1+m_2}$
$x_{cm} = \frac{(8.60~kg)(0.230~m)+(5.25~kg)(0.460~m)}{8.60~kg+5.25~kg}$
$x_{cm} = 0.317~m$
$y_{cm} = \frac{m_1y_1+m_2y_2}{m_1+m_2}$
$y_{cm} = \frac{0+(5.25~kg)(-0.230~m)}{8.60~kg+5.25~kg}$
$y_{cm} = -0.087~m$
Relative to the hip joint, the center of mass is located at the coordinates (0.317 m, -0.087 m).
