Answer
${Y_{cm}} \approx 1.3\,m$
Work Step by Step
We know that the formula for the y coordinate of the center of mass is:
${Y_{c.o.m.}} = \frac{{{m_1}{y_1} + {m_2}{y_2} + {m_3}{y_3}}}{{{m_1} + {m_2} + {m_3}}}$
We also know that:
${m_1} = 3kg$
${m_2} = 4kg$
${m_3} = 8kg$
${y_1} = 0$
${y_2} = 1\,m$
${y_3} = 2\,m$
Substituting these values in the formula and solving:
${Y_{cm}} = \frac{{0 + \left( {4 \times 1} \right) + \left( {8 \times 2} \right)}}{{3 + 4 + 8}} = 1.33\,m$
${Y_{cm}} \approx 1.3\,m$
