An object flying in air with velocity $(10\hat{i} + 15\hat{j} - 5\hat{k})$ suddenly breaks in two pi

Question

An object flying in air with velocity $(10\hat{i} + 15\hat{j} - 5\hat{k})$ suddenly breaks in two pieces whose masses are in the ratio $1 : 4$. The smaller mass flies off with a velocity $(50\hat{i} + 15\hat{j} + 15\hat{k})$. The velocity of the larger piece will be

Professor PC Thomas Classes · Answer

Conservation of momentum: $(m+4m)\vec{v} = m\vec{v}_1 + 4m\vec{v}_2$. $5(10\hat{i} + 15\hat{j} - 5\hat{k}) = (50\hat{i} + 15\hat{j} + 15\hat{k}) + 4\vec{v}_2$. $50\hat{i} + 75\hat{j} - 25\hat{k} = 50\hat{i} + 15\hat{j} + 15\hat{k} + 4\vec{v}_2$. $4\vec{v}_2 = 0\hat{i} + 60\hat{j} - 40\hat{k} \implies \vec{v}_2 = 0\hat{i} + 15\hat{j} - 10\hat{k}$.