A bomb moving with velocity (40 i +50 j -25 k ) m s^ -1 explodes...

( Let the mass of the unexploded bomb be $5 \mathrm{~m}$. It explodes into the two pieces of masses $m and 4 m$ respectively. Initial momentum of the unexploded bomb $=5 m(40 \hat{i}+50 \hat{j}-25 \hat{k})$ After explosion, momentum of the smaller piece $=m \vec{v}_1=m(200 \hat{i}+70 \hat{j}+15 \hat{k})$ and momentum of the larger piece $=4 m \vec{v}_2$ where $\vec{v}_1$ and $\vec{v}_2$ are the velocities of the two pieces respectively. According to the law of conservation of momentum, we get $$\begin{aligned} & 5 m(40 \hat{i}+50 \hat{j}-25 \hat{k})=m(200 \hat{i}+70 \hat{j}+15 \hat{k})+4 m \vec{v}_2 \\ & 4 m \vec{v}_2=5 m(40 \hat{i}+50 \hat{j}-25 \hat{k})-m(200 \hat{i}+70 \hat{j}+15 \hat{k}) \\ & \quad \vec{v}_2=\frac{1}{4}(180 \hat{j}-140 \hat{k})=45 \hat{j}-35 \hat{k}\end{aligned}$$