I'm trying to model the velocity of two objects ($A$ and $B$) of a certain mass and starting speed, after they collide in one dimension in Microsoft Excel. Trouble is, I don't know how to rearrange the equations at the very end of the process to solve for both velocities.
This is part of an assignment question from my university, and since I want to make sure I'm doing it correctly, I'm using the example numbers from my textbook, which is one specially tailored for my university course. I'll try and explain the working out as best I can...
In this case, I know both the masses ($m_A = 4kg$ $m_B = 2kg$) and starting speeds ($u_A = 10m/s$ $u_B=-15m/s$) of the objects, but not their velocity. The Coefficient of Restitution has been set to $0.6$. I know that when two objects collide with one another, their momentum is conserved through this formula:
$$m_Au_A+m_Bu_B = m_Av_A+m_Bv_B$$
Which I've used - like the book - to build the equation $4*10+2*(-15)=4v_A+2v_B$. The answer to this can't simply be $6$, because I haven't figured out what the velocity is yet. So instead, I reverse and solve the equation to get $4vA+2vB=10$.
The last thing I need to get the velocity is the law of restitution (the thing used to properly obtain the $0.6$ from earlier) which is $(v_B-v_A)/(u_A-u_B)$, or in this case $(v_B-v_A)/(-(15)-10)$.
Again, I don't know what the velocities are, so I just make do with $v_B-v_A=15$. So far, so good. The problem comes when the book takes this seemingly giant leap in logic and says that - using the numbers I've found so far - I can solve for velocity as $v_A=-(10/3)=-3.3$ and $v_B=(35/3)=11.7$!
How?! How did they get this result? Where'd that $35$ come from? The book doesn't say. That's what I get for not paying enough attention, I suppose. What I'm looking for is how to rearrange the equations to obtain the two velocities. How'd it go from $v_B-v_A=15$ to the answer? I have the feeling that it's a lot simpler than it appears to be.
Also, I'm sorry if the formatting of this post is a little botched. I'm a programmer by trade, and I've never heard of 'MathJax' or used LaTeX at all before now. If this question would be more appropriate on another area of the site, please let me know.