Glider pulled by suspended mass

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The discussion revolves around a physics problem involving a glider and a hanging mass connected by a string over a pulley. Participants are trying to derive the relationship between the speeds and accelerations of the glider and the hanging mass, specifically vx = uvy and ax = uay. There is confusion regarding the application of differentiation and the chain rule to relate the variables involved. One user expresses frustration after spending several hours on the problem and seeks clarification on the geometric relationships between the variables. The conversation highlights the importance of understanding how changes in one variable affect others in the system.
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Homework Statement



A 1.00-kg glider on a horizontal air track is pulled by a string at an angle θ . The taut
string runs over a pulley and is attached to a hanging object of mass 0.500 kg . (a) Show that the speed vx of the glider and the speed vy of the hanging object are related by vx = uvy, where u = z(z2–h02)–1/2. (b) The glider is released from rest. Show that at that instant the acceleration ax of the glider and the acceleration ay of the hanging object are related by ax = uay.


Homework Equations



vy2+h02=z2 (i think...)

The Attempt at a Solution



having problems with part b)
i tried to obtain vx=uvy by deriving the following equation by t:

vy2+h02=z2

see attachment for my attempt.

i've been working on this one problem for a few hours now... i don't get it
 

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anybody?
 
Draw the triangle incorporating z, ho, and x. What is x in terms of the other variables?

When the hanging mass falls a given distance, what happens to the length of z? How does x change when z changes? How does a change in the length of z relate to the velocity of the falling mass?

Hint: Differentiation is required, and then an application of the chain rule.
 
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