# Elastic and inelastic collision of two objects with arbitrary mass

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An object A moving with velocity V collides with a stationary object B. After the Collision, A is moving with velocity (1/2)V and B with velocity (3/2)V. Find the ratio of their masses.

If, instead of bouncing apart, the two bodies stick together after the collision, with what velocity would they then move?

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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

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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 ...

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