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.