Conservation of energy and momentum Questions
1. A bomb weighing 50kg explodes into 3 pieces in flight when
its velocity is $(20 \hat{i}+ 22 \hat{j} +10 \hat{k}) \ ms^{-1}$. Two fragments of bombs weighing $10 \ kg$ and $20 \ kg$ are found to have velocities of $(100 \hat{i}+ 50 \hat{j} + 20 \hat{k}) \ ms^{-1}$ and $(30 \hat{i} - 20 \hat{j} - 10 \hat{k}) \ ms^{-1}$. Find the velocity of 3rd piece of the bomb.
The bomb is exploding, so no external force act on it. Thus the momentum is conserved.
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Mass of the $3^{rd}$ piece is $20 \ kg$
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Applying conservation of momentum,
$\vec{p_i} = \vec{p_f} \\ $
$50 (20 \hat{i}+ 22 \hat{j} +10 \hat{k}) = 10(100 \hat{i}+ 50 \hat{j} + 20 \hat{k}) + 20(30 \hat{i} - 20 \hat{j} - 10 \hat{k}) + 20\vec{v}$
$\\ \implies \vec{v} = (-30 \hat{i} + 50 \hat{j} + 25 \hat{k}) \ ms^{-1}$