A bomb moving with velocity $(40 \hat{\mathbf{i}}+50 \hat{\mathbf{j}}-25 \hat{\mathbf{k}}) \mathrm{m} /…
A bomb moving with velocity $(40 \hat{\mathbf{i}}+50 \hat{\mathbf{j}}-25 \hat{\mathbf{k}}) \mathrm{m} / \mathrm{s}$ explodes into two pieces of mass ratio $1: 4$. After explosion the smaller piece moves away with velocity $(200 \hat{\mathbf{i}}+70 \hat{\mathbf{j}}+15 \hat{\mathbf{k}}) \mathrm{m} / \mathrm{s}$. The velocity of larger piece after explosion is
$45 \hat{\mathbf{j}}-35 \hat{\mathbf{k}}$
$45 \hat{\mathbf{i}}-35 \hat{\mathbf{j}}$
$45 \hat{\mathbf{k}}-35 \hat{\mathbf{j}}$
$-35 \hat{\mathbf{i}}+45 \hat{\mathbf{k}}$
Solution
From conservation of linear momentum $5 m(40 \hat{\mathbf{i}}+50 \mathbf{j}-25 \hat{\mathbf{k}})$
$=m(200 \hat{\mathbf{i}}+70 \hat{\mathbf{j}}+15 \hat{\mathbf{k}})+4 m(x \hat{\mathbf{i}}+y \hat{\mathbf{j}}+z \hat{\mathbf{k}})$
$\Rightarrow \quad x \hat{\mathbf{i}}+y \hat{\mathbf{j}}+z \hat{\mathbf{k}}=45 \hat{\mathbf{j}}-35 \hat{\mathbf{k}}$