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## Homework Statement

Two identical molecules, A and B, move with the same horizontal velocities but opposite vertical velocities. Which of the following is always NOT true after they collide:

A - the sum of kinetic energy before collision is less than the sum after

B - the sum of kinetic energy before collision is greater than the sum after

C - molecule A will have greater momentum after the collision than molecule B

D - molecule A will have greater vertical velocity than molecule B

## Homework Equations

conservation of momentum: m

_{a}v

_{ai}+m

_{b}v

_{bi}=m

_{a}v

_{af}+m

_{b}v

_{bf}

## The Attempt at a Solution

The answer in the back of the book says "The question does not specify any specific velocities, so assign any number that you like. If both molecules initially have horizontal components of +5m/s and vertical components of +3m/s and -3m/s, then possible values after collision could be horizontal components of +8m/s and +2m/s and vertical components of +10m/s and -10m/s. This would conserve momentum, but not the kinetic energies of the molecules. Kinetic energy does not have to be conserved because you are not told that this is an elastic collision. While the magnitude of the vertical components must remain the same for it to add up to 0, the magnitude of the horizontal components can vary as long as their sum adds up to +10. This implies that either molecule A or B may have a greater horizontal component, and therefore greater overall speed and momentum, so (C) is incorrect. (D) is wrong, because it would violate the law of conservation of momentum."

**I don't understand how this was done at all, I've gone over it multiple times and I'm boggled. Can someone break this answer down for me?**

How were the values of +2, +8, +10, & -10 acquired exactly?

I get that momentum must be conserved in elastic and inelastic collisions, whereas kinetic energy is only conserved in completely elastic collisions. So the equation that applies here is:

m

Since the 2 molecules are identical we can drop all the m's so:

v

from here on I'm stumped :( any clarification would be appreciated!

How were the values of +2, +8, +10, & -10 acquired exactly?

I get that momentum must be conserved in elastic and inelastic collisions, whereas kinetic energy is only conserved in completely elastic collisions. So the equation that applies here is:

m

_{a}v_{ai}+m_{b}v_{bi}=m_{a}v_{af}+m_{b}v_{bf}Since the 2 molecules are identical we can drop all the m's so:

v

_{ai}+v_{bi}= v_{af}+v_{bf}...from here on I'm stumped :( any clarification would be appreciated!