In an elastic collision, a 300 kg bumper car collides directly from behind with a second, identical bumper car that is traveling in the same direction. the initial speed of the leading bumper car is 5.30 m/s and that of the trailing car is 5.90 m/s. assuming that the mass of the drivers is much, much less than that of the bumper cars, what are their final speeds (in m/s)?

If we had:

We will have:

Explanation:

In an elastic collision both linear momentum and kinetic energy are conserved, so we will have:

We will call our bumpers 1 and 2.

For the momentum equation we know that:

Since all the masses are the same (300kg), they cancel out:

For the kinetic energy equation we know that:

Since all the masses are the same (300kg), they cancel out (and also the 2 dividing):

We then must solve this system:

Which we will rewrite as:

The last of these equations can be written as:

But we know that , so those cancel out:

So we can write:

Which means:

Which solving for the final velocity leaves us with:

Grabbing any equation that relates both final velocities easily, for example , we obtain:

So we conclude that the bumpers have just exchanged velocities (something sometimes seen in billiards for example):

d) physical means can be used to separate the components of air.