# 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?

##### 1 Answer

#### Answer:

In an elastic collision, both momentum and kinetic energy are conserved. If we call the

#### Explanation:

Initial momentum:

Initial kinetic energy:

Because this is an elastic collision, both will be conserved:

Final momentum:

Final kinetic energy:

We now have two equations,

Let's double

We can find a value for

Then:

Let's multiply through by 3 for neatness:

Rearranging:

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

If

But wait: this is just the condition **before** the collision! The

If

The minus sign indicates that this velocity is in the opposite direction to the original velocity.

The