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## Worked example 6.5: Elastic collision

Question: An object of mass , moving with velocity , collides head-on with a stationary object whose mass is . Given that the collision is elastic, what are the final velocities of the two objects. Neglect friction.

where and are the final velocities of the first and second objects, respectively. Since the collision is elastic, the total kinetic energy must be the same before and after the collision. Hence,

Let and . Noting that , the above two equations reduce to

and

Eliminating between the previous two expressions, we obtain

or

which has the non-trivial solution . The corresponding solution for is .

It follows that the final velocity of the first object is

The minus sign indicates that this object reverses direction as a result of the collision. Likewise, the final velocity of the second object is

Next: Worked example 6.6: 2-dimensional Up: Conservation of momentum Previous: Worked example 6.4: Bullet
Richard Fitzpatrick 2006-02-02