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Hello! I have solved problem 89 using analytic way, i.e, the length of the string will always be constant, so repeated substitutions and differentiating will make way(i got answer as "c"). But is there any method by using logic that will provide a solution even faster, and is there any technique? Also i am a noob, so can you suggest me a good book (available on the internet free) which goes through these concepts in more detalil?

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    $\begingroup$ The logic in this question is this only that the length of string is constant. So the velocities of two end of string along string will be same. So $2 v_B=v_Acos\theta$. Where $cos \theta = \frac x {\sqrt{x^2+h^2}}$ $\endgroup$ – Tojrah Apr 18 '19 at 5:58
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    $\begingroup$ Hi Shamim and welcome to the Physics SE! Please note that we don't answer homework or worked example type questions. Please see this page in the site help for more on what topics you can ask about here. $\endgroup$ – John Rennie Apr 18 '19 at 6:46
  • $\begingroup$ Sorry i was unaware of it. Should i delete my post? $\endgroup$ – user228422 Apr 18 '19 at 9:00
  • $\begingroup$ @JohnRennie While the statement is taken from a textbook the question itself is really a resource reference. $\endgroup$ – ZeroTheHero Apr 18 '19 at 18:59
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You can consider the case where $x>>h$, then the rate of increase of the length of the part of the string to the right of the fixed pully is $v_A$, so the movable pully raises at a rate of $v_A/2$. Only c provides this limit for large $x$.

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