Question about relative speeds.

[port31]

Lets say I have a moving object that has speed $v_1$
and mass $m_1$ and it collides with a more massive object of
mass $m_2$ And this mass is at rest and when they collide they stick together.
If I use momentum conservation I would get
$m_1 v_1=(m_1+m_2)(v_2)$ and $v_2$ is the speed after the collision
but what if I wanted to analyze this from the rest frame of $m_1$
It would look as if the more massive object was moving at me at a speed $v_1$
So now I would have $m_2(-v_1)=(m_1+m_2)(v_2)$ the final speeds would be different in those 2 cases so what's wrong with my reasoning.

 

[russ_watters]

The final speeds would indeed be different because you are using a different reference frame. To check to make sure there is no conflict, compare the before and after speeds of each object. The difference should be the same regardless of which frame you choose.

 

[Doc Al]

So now I would have $m_2(-v_1)=(m_1+m_2)(v_2)$ the final speeds would be different in those 2 cases so what's wrong with my reasoning.

If you now transform your answer to the original frame (by adding $v_1$) you'll find that the speeds match.