*Answer:* Momentum conservation yields

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