Physics - Center of Mass Question with Solution | TestHub

Since the object is initially at rest, its total initial momentum is zero. By the conservation of linear momentum, the total momentum after the explosion must also be zero. Let $M=5\text{ kg}$. One fragment has mass $m_1=2\text{ kg}$ and velocity $v_1=6\text{ m/s}$. The other fragment has mass $m_2=M-m_1=5\text{ kg}-2\text{ kg}=3\text{ kg}$. Let its velocity be $v_2$. Then $0=m_1{v}_1+m_2{v}_2$. So, $0=(2\text{ kg})(6\text{ m/s})+(3\text{ kg})v_2$. This gives $12+3v_2=0$, so $v_2=-12/3=-4\text{ m/s}$. The negative sign indicates that the second fragment moves in the opposite direction to the first fragment. Thus, its velocity is $4\text{ m/s}$ in the opposite direction.