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Conservation of linear momentum
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An object flying in air with velocity $(20\hat{i}+25\hat{j}-12\hat{k})$ suddenly breaks in two pieces whose masses are in the ratio 1 : 5. The smaller mass flies off with a velocity $(100\hat{i}+35\hat{j}+8\hat{k})$. The velocity of the larger piece will be:$m\vec{v}_0=\frac{m}{6}\vec{v}_1+\frac{5m}{6}\vec{v}_2 \Rightarrow 6(20\hat{i}+25\hat{j}-12\hat{k})=(100\hat{i}+35\hat{j}+8\hat{k})+5\vec{v}_2 \Rightarrow \vec{v}_2=4\hat{i}+23\hat{j}-16\hat{k}$.