An object flying in air with velocity (20i^$$ $$+$$ $$25j^$$ $$-$$ $$12k^) suddenly breaks in two pieces whose masses are in the ratio $$1$$: $$5$$. The smaller mass flies off with a velocity (100i^$$ $$+$$ $$35j^$$ $$+$$ $$8k^). The velocity of the larger piece will be

Question

An object flying in air with velocity (20i^$$ $$+$$ $$25j^$$ $$-$$ $$12k^) suddenly breaks in two pieces whose masses are in the ratio $$1$$: $$5$$. The smaller mass flies off with a velocity (100i^$$ $$+$$ $$35j^$$ $$+$$ $$8k^). The velocity of the larger piece will be

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Let m be the mass of an object flying with velocity v in air. When it gets split into two pieces of masses in ratio $$1$$ : $$5$$, the mass of smaller piece is $$m/6$$ and of bigger piece is $$5m6$$.This situation can be interpreted diagrammatically as below.As, the object breaks in two pieces, so the momentum of the system will remains conserved, i.e. the total momentum (before$$ $$breaking) $$=$$ total momentum (after$$ $$breaking)                     $$mv=m6v1+5m6v2$$⇒$$v=v16+5v26Given$$,  $$v=$$ $$20i^$$ $$+$$ $$25j^$$ $$-$$ $$12k^and$$      $$v1$$ $$=$$ $$100i^$$ $$+$$ $$35j^$$ $$+$$ $$8k^Putting$$ these values in Eq. (i), we $$get(20i^+25j^-12k^)=(100i^+35j^+8k^)6+5v26$$⇒         (120i^+150j^-72k^)=(100i^+35j^+8k^)+5v2$$⇒          $$v2=15(20i^+115j^-80k^)                   $$=4i^$$ $$+$$ $$23j^$$ $$-$$ $$16k^$$

An object flying in air with velocity (20i^ + 25j^ - 12k^) suddenly breaks in two pieces whose masses are in the ratio 1: 5. The smaller mass flies off with a velocity (100i^ + 35j^ + 8k^). The velocity of the larger piece will be

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