A particle of mass m moving in the $$x-direction$$ with speed $$2v$$ is hit by another particle of mass $$2m$$ moving in the $$y-direction$$ with speed v. If the collision is perfectly inelastic, the percentage loss in the Energy during the collision is close to

Question

A particle of mass m moving in the $$x-direction$$ with speed $$2v$$ is hit by another particle of mass $$2m$$ moving in the $$y-direction$$ with speed v.  If the collision is perfectly inelastic, the percentage loss in the Energy during the collision is close to

Infinity Learn · Accepted Answer

apply law of conservation of linear momentum sum of momentum of both bodies before collision $$=sum$$ of momentum of both bodies after collision  m $$2v$$⋅i∧ $$+$$ $$2m$$ v⋅j∧  $$=$$   (m+2m)⋅v¯' here v¯' if final velocity of both bodies as they stick together∴   v¯'  $$=$$    $$2v3(i$$∧$$+j$$∧$$)$$ Energy $$final=Efinal$$  $$=$$   $$12$$ $$(3m)v$$'$$2$$  $$=$$   $$3m2$$ $$(223v)2$$  $$=$$    $$43mv2$$    ∴     percentage loss of $$energy=Einitial$$−EfinalEinitial×$$100$$   percentage loss of $$energy=$$     $$3mv2$$−$$43mv23mv2$$ × $$100$$  percentage loss of $$energy=$$    $$59$$ ×$$100$$  percentage loss of energy ≃  $$56$$%

A particle of mass m moving in the x-direction with speed 2v is hit by another particle of mass 2m moving in the y-direction with speed v. If the collision is perfectly inelastic, the percentage loss in the Energy during the collision is close to

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