Dependent motion with ropes question

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The discussion centers on solving a dependent motion problem involving ropes, where the user struggles with the relationship between velocities and geometry. The user correctly identifies that the sum of the lengths of the ropes, represented as Sa + Sb = L1, leads to the conclusion that Va = -Vb when differentiating with respect to time. The user also attempts to express the position X in terms of SA and the angle theta, indicating a need for clarity in relating velocity to geometric relationships.

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I attached the problem with my attempt. I think the geometry I used is correct but I am getting the wrong answer. When I take the flip Va/V (as shown in my attempt) I get the right answer. I am not even sure if I can relate velocity with a triangle.

The method I used is based on the fact that Sa + Sb = L1 so when you take the time derivative you get Va = -Vb.
 

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X=SA cos(theta). As X increases in the rate of 1.5 m/s, both SA and theta change. It is not true that V=VA.

Write out YB in terms of X, and find the derivative with respect the time. ehild
 

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