Momentum and Kinetic Energy Question

[craig.16]

Homework Statement

Two bodies approach each other with the same speed of 2 m/s and collide head-on in an
inelastic collision. The mass of one body is m, the other has mass 3m. After the collision, the
lighter body has rebounded to travel back along its original trajectory with speed 1 m/s.
(i) What is the speed and direction of the heavier body after the collision?
(ii) How much kinetic energy was lost in the collision?
(iii) After the collision, the lighter body is brought to rest by the application of a variable
force. Calculate the work done by this force on the lighter body.

Homework Equations

m(1)u(1)+m(2)u(2)=m(1)v(1)+m(2)v(2)
KE(before) does not equal KE(after)

The Attempt at a Solution

if I take the right as the positive x direction and take the lighter mass to be traveling right therefore implying the heavier mass to be traveling left as its a head on collision I get:
2m+3m(-2)=m(-1)+3mv
2m-6m=-m+3mv
-3m=3mv
v=-1m/s

If instead I take the heavier mass to be traveling right and the lighter mass to be traveling left I get:
3m(2)+m(-2)=3mv+m(1)
6m-2m=3mv+m
3m=3mv
v=1m/s

The problem isn't necessarily which one is right but the fact that if any of these are right then that would imply that its an elastic collision as the minus sign would be squared out from the first answer. Clearly I've done a small error somewhere like a minus sign or a plus sign within my calculation or maybe its a wrong sign in what I believe to be the equation for working out loss of kinetic energy. Any help on what I have done wrong and providing a full equation to work out loss of kinetic energy will be much appreciated just to double check I haven't got the equation wrong.

 

[Beaker87]

BOTH answers are correct, and in fact state the same thing:

They both say that after the collision, the heavier object is moving in the same direction it started moving at 1m/s.

In order to find the loss of kinetic energy, try calculating the kinetic energy of each object before the collision, and after the collision. How much less energy is there after the collision than there was before the collision?

 

[craig.16]

Is the answer for loss of kinetic energy:

Spoiler

6J

because if so I know what I did wrong in the kinetic energy equation.