A shell at rest at the origin explodes into t | vedclass

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(B) Since the shell is initially at rest,the initial momentum is zero. According to the law of conservation of linear momentum,the final vector sum of

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$5$

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(B) Since the shell is initially at rest,the initial momentum is zero. According to the law of conservation of linear momentum,the final vector sum of the momenta of the fragments must be zero.Let $\vec{p}_1$,$\vec{p}_2$,and $\vec{p}_m$ be the momenta of the three fragments.$\vec{p}_1 = 1 	imes 5 \hat{i} = 5 \hat{i} \ kg \cdot m/s$$\vec{p}_2 = 2 	imes 6 \hat{j} = 12 \hat{j} \ kg \cdot m/s$$\vec{p}_m = m \vec{v}_m$Since $\vec{p}_1 + \vec{p}_2 + \vec{p}_m = 0$,we have $\vec{p}_m = -(\vec{p}_1 + \vec{p}_2) = -(5 \hat{i} + 12 \hat{j})$.The magnitude of the momentum of the $m \ kg$ piece is $|\vec{p}_m| = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \ kg \cdot m/s$.Given the speed of the $m \ kg$ piece is $6.5 \ m/s$,we have $m 	imes 6.5 = 13$.Thus,$m = \frac{13}{6.5} = 2 \ kg$.The total mass of the shell is $M = 1 + 2 + m = 1 + 2 + 2 = 5 \ kg$.

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