(Solved): 5.2.15. [Level 2] In the depths of gravity-free space, an asteroid of mass m0 is observed at t=0 ...

5.2.15. [Level 2] In the depths of gravity-free space, an asteroid of mass $m_0$ is observed at $t=0$ to pass through the coordinates $(0,0,0)$ with velocity $10j\mathrm{m}/\mathrm{s}$. Later, an explosive charge is detonated within the asteroid, breaking it into three distinct pieces- $A,B,C$-with masses $m_A=0.5m_0,m_B=0.3m_0$, and $m_C=0.2m_0$. At $t=t_1$, ${\mathbf{v}}_A=(?20\mathbf{i}+10\mathbf{j})\mathrm{m}/\mathrm{s},{\mathbf{v}}_B=(33.\overline{3}\mathbf{i}+10\mathbf{j})\mathrm{m}/\mathrm{s},{\mathbf{v}}_C=(v_{C_1}\mathbf{i}+$ $v_{C_2}\mathbf{j}+v_{C_3}\mathbf{k})\mathrm{m}/\mathrm{s},{\mathbf{r}}_{A_{/O}}=\left(?20\mathbf{i}+y_A\mathbf{j}\right)\mathrm{m},{\mathbf{r}}_{B_{/O}}=(33.3\mathbf{i}+$ $20\mathbf{j})\mathrm{m}$, and ${\mathbf{r}}_{c_{C_O}}=20\mathbf{j}\mathrm{m}$. a. Use mass center and linear momentum concepts to determine $v_C$ and $y_A$. b. Verify that the angular momentum about $O$ is zero, even after the asteroid has split up.