Question

Find acceleration of com of two masses 1kg and 2kg having acceleration $\overrightarrow{a_1}=2\hat{i}+3\hat{j}$ and $\overrightarrow{a_2}=\hat{i}-\hat{j}+2\hat{k}$ respectively.

Answer 1

Acceleration of COM: $\overrightarrow{a_{COM}}=\frac{m_1\overrightarrow{a_1}+m_2\overrightarrow{a_2}}{m_1+m_2}$

$=\frac{1(2\hat{i}+3\hat{j})+2(\hat{i}-\hat{j}+2\hat{k})}{1+2}$

$=\frac{2\hat{i}+3\hat{j}+2\hat{i}-2\hat{j}+4\hat{k}}{3}$

$=\frac{4\hat{i}+\hat{j}+4\hat{k}}{3}$

$=\frac{4}{3}\hat{i}+\frac{1}{3}\hat{j}+\frac{4}{3}\hat{k}$