how is this equation derived

V'2= V1(2M1)/(M1+M2) (elastic collision - where one object is moving and the other is stationary)

1 answer

It is derived by requiring that both momentum and kinetic energy be conserved.

The center of mass moves forward at velocity vcm = M1*V1/(M1 + M2). After collision, the CM retains that velocity but the velocities change directions in CM-fixed coordinates.

In CM-fixed coordinates,
v2 = -V1*M1/(M1+M2)
v2' (after collision) = V1*M1/(M1+M2)

In lab-fixed coordinates
V2' = v2 -vcm
= 2 V1*M1/(M1+M2)