Physics - Center of Mass Question with Solution | TestHub

The total momentum before the explosion is zero since the firecracker is at rest. By conservation of momentum, the total momentum after the explosion must also be zero. Let $M=200\text{ g}=0.2\text{ kg}$. One piece has mass $m_1=120\text{ g}=0.12\text{ kg}$ and velocity $v_1=10\text{ m/s}$ (east). The other piece has mass $m_2=M-m_1=0.2-0.12=0.08\text{ kg}$. Let its velocity be $v_2$. Then $0=m_1{v}_1+m_2{v}_2$. So, $0=(0.12\text{ kg})(10\text{ m/s})+(0.08\text{ kg})v_2$. This gives $1.2+0.08v_2=0$, so $v_2=-1.2/0.08=-15\text{ m/s}$. The negative sign indicates the direction is opposite to $v_1$, i.e., west. Thus, the velocity is $15\text{ m/s}$ to the west.