relativity question

[bruteforce]

1. The problem statement, all variables and given/known data

We have two objects of mass m1. The first object is moving towards the second and has speed u. After they collide, they stick together and move as one mass with speed v.
Now what is the resulting mass and what is v?


2. Relevant equations




3. The attempt at a solution

I used that the energy is conserved and the equation E^{2}=(mc^{2})^{2}+(pc)^{2}

But I don't get the correct answer

[kuruman]

Is the second object at rest? Regardless of the answer to this question, you need to conserve momentum. This is an inelastic collision and unless you can account for the energy that is dissipated as heat during the collision, you cannot conserve energy.

[bruteforce]

the second one is at rest, and there is no energy loss.

[kuruman]

OK, if there is no energy loss, then total relativistic energy is conserved. You need to say with an equation that

Energy before = Energy after

and with another equation that conserves momentum:

Momentum before = Momentum after

This will give you two equations and you have two unknowns, the final velocity and the final mass.