Dot product issue. system of equations

[bcddd214]

Homework Statement

As illustrated, a ball of mass m_1=0.25 kg and velocity V_(0_1=+5.00 m/s) collides head on with a ball of mass m_2=0.8 kg that is initially at rest. No external forces act on the balls. If the collision is elastic, what are the velocities of the balls after they collide?

Homework Equations

V_(0_1 )
p_i=p_f
〖KE〗_i=〖KE〗_f

The Attempt at a Solution

m_1 v_(1_i )+0=m_2 v_(2_f )+m_1 v_(1_f )
1/2 m_1 〖v_(1_i )〗^2=1/2 m_1 〖v_(1_f )〗^2+1/2 m_2 〖v_(2_f )〗^2
A ⃑*B ⃑=■(i ̂&j ̂&k ̂@A_x&A_y&A_z@B_x&B_y&B_z )=|■(A_y&A_z@B_y&B_x )| i ̂+
I get a total brain fart once I plug it into the matrix...? :(

 

[ideasrule]

A ⃑*B ⃑=■(i ̂&j ̂&k ̂@A_x&A_y&A_z@B_x&B_y&B_z )=|■(A_y&A_z@B_y&B_x )| i ̂+
I get a total brain fart once I plug it into the matrix...? :(

That last line doesn't seem to render well on my computer, but why do you need to plug anything into a matrix? You have:
m_1 v_(1_i )+0=m_2 v_(2_f )+m_1 v_(1_f )

and:

1/2 m_1 〖v_(1_i )〗^2=1/2 m_1 〖v_(1_f )〗^2+1/2 m_2 〖v_(2_f )〗^2

You know v_1_i, and you just need to solve for either v_1_f or v_2_f. Expressing one of them in terms of the other using the first equation, then plugging the result into the second, should give you the result.

 

[bcddd214]

I am sooo physics paranoid. I hit the table and freeze because I keep getting it wrong for some reason.

A*B=A_x, A_y, A_z= |A_y, A_z|i
_____B_x, B_y, B_z |B_y, B_x|

I get here, I seem to be on a roll, and then just freeze. :(

 

[ideasrule]

I still don't understand why you're using matricies. What's A and B? Why are you multiplying them together?

You already got 2 equations, and you have only 2 unknowns. Direct substitution should be all you need to get the answer. If you're trying to use Gaussian elimination, it doesn't work because this isn't a linear system of equations.