An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $$1$$ kg moves with a speed $$of12$$ ms−$$1and$$ the second part of mass $$2$$ kg moves with $$8$$ ms−$$1speed$$. If the third part flies off $$with4$$ ms−$$1speed$$, then its mass is

Question

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $$1$$ kg moves with a speed $$of12$$  ms−$$1and$$ the second part of mass $$2$$ kg moves with $$8$$  ms−$$1speed$$. If the third part flies off $$with4$$  ms−$$1speed$$, then its mass is

Infinity Learn · Accepted Answer

The situation is as shown in the figure.According to law of conservation of linear momentump¯$$1+p$$¯$$2+p$$¯$$3=0$$ ∴    p¯$$3=$$−p¯$$1+p$$¯$$2$$ Here p¯$$1=1$$ $$kg12$$ ms−$$1i^=12i^kg$$ ms−$$1$$ p¯$$2=2$$ $$kg8$$ ms−$$1j^=16j^kg$$ ms−$$1$$ ∴  p¯$$3=$$−$$12i^+16j^kg$$ ms−$$1$$ The magnitude of p¯$$3$$ is p¯$$3=122+162=20$$ kg ms−$$1$$ ∴  $$m3=p3v3=20$$ kgms−$$14$$ ms−$$1=5kg$$

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of12 ms−1and the second part of mass 2 kg moves with 8 ms−1speed. If the third part flies off with4 ms−1speed, then its mass is

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