Why Does Cramster Simplify Velocity Components Incorrectly in Physics Problems?

[Fellowroot]

Homework Statement

This problem is from Modern Physics by Kenneth Krane 2nd ED

The problem is:

An atom of mass m moving in the x direction with speed v collides elastically with an atom of mass 3m at rest. After the collision the first atom moves in the y direction. Find the direction of motion of the second atom and the speeds of both atoms in terms of v after the collision.

Now my question is not how to solve this problem, it is to try and understand a math step involved in this problem from a solution off of cramster.

Homework Equations

The Attempt at a Solution

On cramster they reduce this:

9v$^{2}_{}$cos$^{2}$(x)+9v$^{2}_{}$cos$^{2}$(x)

to this:

9v$^{2}$

But when I did the problem and got down to their step I have this:

9v$^{2}_{x}$cos$^{2}$(x)+9v$^{2}_{y}$cos$^{2}$(x)

Those velocities are different components an x and a y, which they neglected to distinguish on cramster.

I know that:

3cos$^{2}$(x) + 3sin$^{2}$(x) = 3

But I don't see how they came to their conclusion because the x and y components could be different.

Thanks.

 

[vela]

If your equation is correct, you're right that it can't be reduced. Show us how you got your equation.

 

[Fellowroot]

There is about 3 pages of work to get to that equation but I don't think I have made a mistake. So its pretty hard to post it. Also if I go by their solution they actually get the correct answer in the end but at the same time I'm very sure that they are indeed two different components. Thanks though.

 

[vela]

Well, I'll just say your equation looks wrong. You almost always get v_x or v cos θ, not the combination v_xcos θ. Similarly, for the y-component.