A ball with a mass of # 3# # kg# is rolling at #18 # #ms^-1# and elastically collides with a resting ball with a mass of #9 # #kg#. What are the post-collision velocities of the balls?
In an elastic collision, both momentum and kinetic energy are conserved. If we call the
Initial kinetic energy:
Because this is an elastic collision, both will be conserved:
Final kinetic energy:
We now have two equations,
We can find a value for
Let's multiply through by 3 for neatness:
Solve using the quadratic formula or otherwise, and you get:
There are actually two roots, therefore,
That is, the second ball, with a mass of
We should solve
But wait: this is just the condition before the collision! The
The minus sign indicates that this velocity is in the opposite direction to the original velocity.