Particle A of mass $$m1$$ moving with velocity $$3i^+j^$$ ms−$$1$$ collides with another particle B of mass $$m2$$ which is at rest initially. Let $$V1$$→ and $$V2$$→ be the velocities of particles A and B after collision respectively. If $$m1=2m2$$ and after collision $$V1$$→$$=i^+3j^ms$$−$$1$$ , the angle between $$V1$$→ and $$V2$$→ is

Question

Particle A of mass  $$m1$$ moving with velocity $$3i^+j^$$ ms−$$1$$  collides with another  particle B of mass  $$m2$$ which is at rest initially.  Let $$V1$$→ and $$V2$$→  be the velocities of particles A and B after collision respectively.  If  $$m1=2m2$$ and after collision $$V1$$→$$=i^+3j^ms$$−$$1$$ , the angle between  $$V1$$→  and $$V2$$→  is

Infinity Learn · Accepted Answer

Let  V→$$2=Vxi^+Vyj^Applying$$ momentum conservation along  x and y direction,$$m1$$×$$3=m1+m2Vx$$ ⇒$$Vx=23$$−$$1$$  And  $$m1=3m1+m2Vy$$ ⇒$$Vy=$$−$$23$$−$$1So$$  V→$$2=23$$−$$1i^$$−$$23$$−$$1j^$$, which is making angle $$45$$° with x axis as shownand V→$$1$$ $$=i^+3j^$$ , is making $$600$$ with x axis as shown in figure So angle between  V→$$1$$ and V→$$2$$ is $$105$$°

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