# Simpler equation for perfectly elastic collisions.

Perfectly elastic collisions problems usually involve calculating the final velocities of two masses from their initial momenta. Trying to derive such formula I got a different result, a shorter formula to solve the same problem:
Take two masses a and b with their respective initial volocities;
First I assumed the velocity of the center of mass to be constant;
vc=const.
Then I moved my referential to the mass a. In this referential I assumed that the absolute value of the relative velocites between the mass a and the center of mass to be also constant.
What I imagined what more or less like this:
Before the collision I would see the center of mass move towards my referential with a velocity "via-vc". After the collision I would see the center of mass move in the opposite direction with the same speed;
Based on this what I got was:
|via-vc|=|vfa-vc|=const.
via-vc=vc-vfa
via+vfa=2*vc
That's it. The oddity is that it uses a rather faster thought, works perfectly and I've never seen before.
Now you can solve collisions problems with a quicker equation :)

Related Classical Physics News on Phys.org
Doc Al
Mentor
That works. Another equation that you may find useful is the following (quoting from our Introductory Physics Formulary entry on Linear Momentum and Collisions):

Special Case: Elastic Collisions in one dimension:

For a perfectly elastic straight-line collision, the relative velocity is reversed during the collision:

$$v_1 - v_2 = v_2' - v_1'$$​