Answer
$3.575\times 10^{-11}m$
Work Step by Step
We can find the required X and Y coordinates of the center of mass of the molecule as follows:
Due to symmetry, the x-coordinate of the center of mass is:
$X_{CM}=0$
and the y-coordinate of the center of mass is:
$Y_{CM}=\frac{\Sigma my}{M}$
$Y_{CM}=\frac{m_{\circ}y_1+m_{\circ}y_2+m_s y_3}{m_{\circ}+m_{\circ}+m_s}$
This simplifies to:
$Y_{CM}=\frac{m_{\circ}(y_1+y_2)+m_sy_3}{2m_{\circ}+m_s}$
$Y_{CM}=\frac{2m_{\circ}(y_1)+m_sy_3}{2m_{\circ}+m_s}$ $(As y_1=y_2)$
We plug in the known values to obtain:
$Y_{CM}=\frac{2(16u)(0.143nm)sin30^{\circ}+(32u)(0)}{2(16u)+32u}$
$Y_{CM}=3.575\times 10^{-11}m$
