Glider pulled by suspended mass

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SUMMARY

The discussion centers on the relationship between the speeds and accelerations of a glider and a hanging mass in a physics problem involving a pulley system. Specifically, it establishes that the speed of the glider (vx) and the speed of the hanging object (vy) are related by the equation vx = uvy, where u = z(z²–h₀²)⁻¹/². Furthermore, it demonstrates that the acceleration of the glider (ax) and the acceleration of the hanging object (ay) are related by ax = uay. The problem requires differentiation and the application of the chain rule to derive these relationships.

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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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