Answer
The y-coordinate of the molecule's center of mass is $~~3.13\times 10^{-11}~m$
Work Step by Step
By symmetry, the center of mass of the three hydrogen atoms is at the origin. Thus the y-coordinate of the center of mass of the three hydrogen atoms is $y = 0$
We can find the y-coordinate of the nitrogen atom:
$y = \sqrt{L^2-d^2}$
$y = \sqrt{(10.14\times 10^{-11}~m)^2-(9.40\times 10^{-11}~m)^2}$
$y = 3.80\times 10^{-11}~m$
Let $m_h$ be the mass of each hydrogen atom.
Then the mass of the nitrogen atom is $13.9~m_h$
We can find the y-coordinate of the molecule's center of mass:
$y_{com} = \frac{(13.9~m_h)(3.80\times 10^{-11}~m)+(3m_h)(0)}{3m_h+13.9m_h}$
$y_{com} = 3.13\times 10^{-11}~m$
The y-coordinate of the molecule's center of mass is $~~3.13\times 10^{-11}~m$.
