A ball of mass 0.193 kg has a velocity of 1.45 i m/s; a ball of mass 0.290 kg has a velocity of -0.407 i m/s. They meet in a head-on elastic collision. Find the speed of their center of mass after the collision.

Use the Principle of Conservation of Momentum :

m1u1 + m2u2 = m1v1 + m2v2

(0.199)(1.49) + (0.298)(-0.392) = (0.199)v1 + (0.298)v2 (1)

Also

since the collision is elastic, e = 1

So

(u1 - u2) = (v2 - v1)

v2 - v1 = 1.882 (2)

Solve (1) and (2) to get v1 and v2

(b) Velocity of Center of Mass before collision

V = (m1u1 + m2u2) / (m1 + m2)

Since there is no external force on the system, the velocity of the center of mass remains unchanged after the collision.

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