Explanation

(a) Here, $m_{1} = 1$ kg, ${\overrightarrow{v}}_{1} = 2\widehat{i}$
$m_{2} = 2$ kg, ${\overrightarrow{v}}_{2} = 2\cos 30\widehat{i} - 2\sin{30\widehat{j}}$
${\overrightarrow{v}}_{CM} = \frac{m_{1}{\overrightarrow{v}}_{1} + m_{2}{\overrightarrow{v}}_{2}}{m_{1} + m_{2}}$
$= \frac{1 \times 2\widehat{i} + 2(2\cos{30{^\circ}\widehat{i} - 2\sin{30{^\circ}\widehat{j}}})}{1 + 2}$
$= \frac{2\widehat{i} + 2\sqrt{3}\widehat{i} - 2\widehat{j}}{3} = \left( \frac{2 + 2\sqrt{3}}{3} \right)\widehat{i} - \frac{2}{3}\widehat{j}$