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:(adsbygoogle = window.adsbygoogle || []).push({});

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 :)

Did you knew about this equation? Tell me what you think.

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# Simpler equation for perfectly elastic collisions.

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