Dependent motion with ropes question

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The discussion focuses on a homework problem involving dependent motion with ropes, where the user struggles with their approach to the geometry of the problem. They believe their geometric interpretation is correct but are getting incorrect results, particularly when relating velocities. The user mentions using the relationship Sa + Sb = L1 and deriving Va = -Vb, but questions the validity of relating velocity to a triangle. They also note that as X increases at a rate of 1.5 m/s, both SA and theta are changing, complicating the relationship. The thread emphasizes the need to express YB in terms of X and find its time derivative for a clearer solution.
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Homework Statement


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
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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