Let       u1, u2 = Velocities of colliding bodies before impact (u1 > u2)

            v1, v2 = Velocities of the colliding bodies after impact

From the law of conservation of momentum

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

Since the impact is between equal masses,

$m_1=m_2=m\\ Then \\ u_1+u_2=v_1+v_2.....................................(i)$

The relation for coefficient of restitution gives;

$e=\dfrac{v_2-v_1}{u_1-u_2}$

Since the impact is perfectly elastic e=1 and accordingly

$u_1-u_2=v_2-v_1 .................(ii)$

Solving equation (i) and (ii) we get;

$v_2=u_1\ \ \ \ \ and \ \ \ \ \ v_1=u_2\ \ which \ shows \ that \ the\ masses\ exchange\ velocitities\ after\ elastic\ impact. $

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