How Do You Calculate Total Momentum of Two Connected Rocks in Motion?

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Homework Statement


Two rocks are tied together with a string of negligible mass, and thrown into the air. At a particular instant, rock 1, which has a mass of 0.2 kg, is headed straight up with a speed of 2 m/s, and rock 2, which has a mass of 0.35 kg, is moving parallel to the ground, in the +x direction, with a speed of 8.5 m/s.

What is the total momentum of the system consisting of both rocks and the string?


Homework Equations





The Attempt at a Solution

 
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This figure is from "Introduction to Quantum Mechanics" by Griffiths (3rd edition). It is available to download. It is from page 142. I am hoping the usual people on this site will give me a hand understanding what is going on in the figure. After the equation (4.50) it says "It is customary to introduce the principal quantum number, ##n##, which simply orders the allowed energies, starting with 1 for the ground state. (see the figure)" I still don't understand the figure :( Here is...
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The last problem I posted on QM made it into advanced homework help, that is why I am putting it here. I am sorry for any hassle imposed on the moderators by myself. Part (a) is quite easy. We get $$\sigma_1 = 2\lambda, \mathbf{v}_1 = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \sigma_2 = \lambda, \mathbf{v}_2 = \begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \\ 0 \end{pmatrix} \sigma_3 = -\lambda, \mathbf{v}_3 = \begin{pmatrix} 1/\sqrt{2} \\ -1/\sqrt{2} \\ 0 \end{pmatrix} $$ There are two ways...
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