Question

Ball 1, with a mass of 120g and traveling at 15m/s , collides head on with ball 2, which has a mass of 310g and is initially at rest.

What are the final velocities of each ball if the collision is perfectly elastic?

Answer 1

According to law of conservation of momentum

          m1 u1 + m2 u2 = m1 v1 + m2 v2

            m1 ( u1 - v1 ) = m2 ( v2 - u2 )                        ...... (1)

From the conservation of energy

           m1 ( u1^2 - v1^2 ) = m2 ( v2^2 - u2^2 )

From the above two equations

         u1 + v1 = u2 + v2

                 v1 = v2 - 15 m/s

From equation (1)

        2 (0.120 kg) (15 m/s) = ( m1 +m2 ) v2

                 v2 = 3.6 / (0.12 +0.31) = 8.37 m/s

                  v1 = 8.37 - 15 = - 6.62 m/s