A sphere A of mass m moving with a velocity hits another stationary sphere B of same mass. If the ratio of the velocities of the sphere after collision is vAvB $$=$$ $$1-e1+e$$ where e is the coefficient of restitution, what is the initial velocity of spheres A with which it strikes?

Question

A sphere A of mass m moving with a velocity hits another stationary sphere B of same mass. If the ratio of the velocities of the sphere after collision is vAvB $$=$$ $$1-e1+e$$ where e is the coefficient of restitution, what is the initial velocity of spheres A with which it strikes?

Infinity Learn · Accepted Answer

vAvB $$=$$ $$1-e1+e$$          vAvB $$-$$ $$1$$ $$=$$ $$1-e1+e$$ $$-$$ $$1$$ or $$vB-vA$$ $$=$$ $$2e1+e$$.$$vB--------(i)But$$ e $$=$$ $$vB-vAu------(ii)or$$ u $$=$$ $$2evBe(1+e)$$   ⇒ $$u+eu$$ $$=$$ $$2vBor$$  u $$+$$ (vB-vA) $$=$$ $$2vB$$   ⇒ u $$=$$ vA $$+$$ vB

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A sphere A of mass m moving with a velocity hits another stationary sphere B of same mass. If the ratio of the velocities of the sphere after collision is vAvB = 1-e1+e where e is the coefficient of restitution, what is the initial velocity of spheres A with which it strikes?

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