An object flying in air with velocity (20 hat | vedclass

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(A) According to the law of conservation of linear momentum,the total momentum before the break is equal to the total momentum after the break.Let the

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$4 \hat{i}+23 \hat{j}-16 \hat{k}$

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(A) According to the law of conservation of linear momentum,the total momentum before the break is equal to the total momentum after the break.Let the total mass be $M = m_1 + m_2$. Given the ratio $m_1 : m_2 = 1 : 5$,we have $m_1 = \frac{M}{6}$ and $m_2 = \frac{5M}{6}$.Initial momentum: $P_i = M \vec{v}_0 = M(20 \hat{i} + 25 \hat{j} - 12 \hat{k})$.Final momentum: $P_f = m_1 \vec{v}_1 + m_2 \vec{v}_2 = \frac{M}{6}(100 \hat{i} + 35 \hat{j} + 8 \hat{k}) + \frac{5M}{6} \vec{v}_2$.Equating $P_i = P_f$:$M(20 \hat{i} + 25 \hat{j} - 12 \hat{k}) = \frac{M}{6}(100 \hat{i} + 35 \hat{j} + 8 \hat{k}) + \frac{5M}{6} \vec{v}_2$Dividing by $M$ and multiplying by $6$:$6(20 \hat{i} + 25 \hat{j} - 12 \hat{k}) = (100 \hat{i} + 35 \hat{j} + 8 \hat{k}) + 5 \vec{v}_2$$120 \hat{i} + 150 \hat{j} - 72 \hat{k} = 100 \hat{i} + 35 \hat{j} + 8 \hat{k} + 5 \vec{v}_2$$5 \vec{v}_2 = (120 - 100) \hat{i} + (150 - 35) \hat{j} + (-72 - 8) \hat{k}$$5 \vec{v}_2 = 20 \hat{i} + 115 \hat{j} - 80 \hat{k}$$\vec{v}_2 = 4 \hat{i} + 23 \hat{j} - 16 \hat{k}$.

An object flying in air with velocity $(20 \hat{i}+25 \hat{j}-12 \hat{k})$ suddenly breaks into 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:

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