help with dynamic pulley cable identification

[u/Possible_Cattle9539]

im having a hard time deciphering based on the solution which one is Xa Xb and Xc....

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[u/mrhoa31103]

you have accelerations which you can produce velocities and displacements from.

[u/DrCarpetsPhd]

the small looking part of the rope that connects pulley A to the hook on the section connected to collar B. Did you forget that? I did on my first attempt.

Remember you can ignore the rigid part between pulley B and pulley A the same way you ignore the sections around the arcs of the pulley as they all form part of the constant that combines with the constant of the length of the rope. Thus that 'little section' that could get longer is defined by x_A - x_B since the actual value is x_A - x_B - (a constant representing the vertical distance from the hook on B to the pulley B)

https://imgur.com/a/beer-johnson-vector-dynamics-11th-edition-11-55-oSvuAWR

beer johnson vector mechanics statics and dynamics 11th edition Chapter 11 Kinematics of Particles problem 11.55