If, instead of bouncing apart, the two bodies stick together after the collision, with what velocity would they then move?
Before the collision:
Object A mass=m1 velocity = v1i
Object B mass=m2 velocity = 0 (rest)
After the collision:
Object A mass=m1 velocity = v1f
Object B mass=m2 velocity = v2f
In an elastic collision, the kinetic energy and linear momentum of each colliding body may change, but the total kinetic energy and the total linear momentum of the system remain the same.
According to the conservation of the total linear momentum,
m1v1i = m1v1f + m2v2f -------(1)
According to the conservation of the total kinetic energy,
(½)m1[(v1i)^2] = (½)m1[(v1f)^2] + (½)m2[(v2f)^2] ---------(2)
Equation (1) can be written as
m1(v1i - v1f) = m2v2f ...
Detailed explanation of equations and solution.