Dynamics, dependent motion analysis

[mathmannn]

Homework Statement

All of this is in the attachment, but here is the question anyways.

"Two blocks of masses A, 50 kg and B, 30 kg are connected to a mass*less pulley which is connected to a wall. Determine the velocity of block B after it moves 0.5 m from its original position. Assume no friction and that the blocks start from rest"

Homework Equations

The Attempt at a Solution

Obviously, I don't need help finding a solution but I can not wrap my head around how my professor got the relationship that $v_A = v_B$. I see that the length of the movement of one block is equal to the other, but why do they have the same sign?

If we define the positive x-axis to be in the direction that block A moves "down" (towards the right) then block B would move "up" so their position and their velocities would have to be opposite of each other?

Can anyone explain to help me see what is going on?

 

[cepheid]

Homework Statement

All of this is in the attachment, but here is the question anyways.

"Two blocks of masses A, 50 kg and B, 30 kg are connected to a mass*less pulley which is connected to a wall. Determine the velocity of block B after it moves 0.5 m from its original position. Assume no friction and that the blocks start from rest"

Homework Equations

The Attempt at a Solution

Obviously, I don't need help finding a solution but I can not wrap my head around how my professor got the relationship that $v_A = v_B$. I see that the length of the movement of one block is equal to the other, but why do they have the same sign?

If we define the positive x-axis to be in the direction that block A moves "down" (towards the right) then block B would move "up" so their position and their velocities would have to be opposite of each other?

Can anyone explain to help me see what is going on?

The solution clearly shows that the vectors for v_A and v_B are in opposite directions (I'm talking about the arrows in the diagram).

The statement v_A = v_B could have been referring to the magnitudes of the velocities. After all, there are no vector arrows over the symbols for the quantities, suggesting that they are meant to be scalars.

 

[The Anonymous]

As a general rule, you define the direction of motion of any object to be the positive direction. Imagine if you unwound the string from around the pulley and laid the two blocks out on a flat surface. In that case you would clearly see that pulling on one block makes them both move in the same direction.
Your professor chose a coordinate system that would result in a consistent direction of motion for both objects. If one block moves down (positive direction) the other one must move up (positive direction).

cheers