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Question Number 20344 by Tinkutara last updated on 25/Aug/17

$$\mathrm{Determine}\mathrm{the}\mathrm{speed}\mathrm{with}\mathrm{which}\mathrm{block}$$$$B\mathrm{rises}\mathrm{in}\mathrm{figure}\mathrm{if}\mathrm{the}\mathrm{end}\mathrm{of}\mathrm{the}\mathrm{cord}\mathrm{at}$$$$A\mathrm{is}\mathrm{pulled}\mathrm{down}\mathrm{with}\mathrm{a}\mathrm{speed}\mathrm{of}2\mathrm{m}/\mathrm{s}.$$

Commented by Tinkutara last updated on 25/Aug/17

Commented by ajfour last updated on 25/Aug/17

$$0.5m/s.$$$$ifblockrisesbyy,thenEgoes$$$$upbyy,andCcomesdownbyy.$$$$lengrhofropethatavailablefor$$$$pull=4y=x\left(say\right)$$$$now4\left(\frac{dy}{dt}\right)=\frac{dx}{dt}$$$$4v_{block}=2m/s$$$$v_{block}=0.5m/s.$$

Commented by Tinkutara last updated on 25/Aug/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

Answered by Tinkutara last updated on 27/Aug/17

Commented by Tinkutara last updated on 27/Aug/17

$$\mathrm{This}\mathrm{is}\mathrm{my}\mathrm{try}!\mathrm{Please}\mathrm{do}\mathrm{not}\mathrm{delete}$$$$\mathrm{your}\mathrm{own}\mathrm{solution}\mathrm{ajfour}\mathrm{Sir}.$$

Commented by Tinkutara last updated on 27/Aug/17

$$\mathrm{Total}\mathrm{length}\mathrm{of}\mathrm{string}$$$$=3x+4(y-x)=4y-x=C$$$$\mathrm{Differentiating}\mathrm{w}.\mathrm{r}.\mathrm{t}\mathrm{time},$$$$4v_B=v_A$$$$\Rightarrow v_B=2\mathbf{÷}4=0.5\mathrm{m}/\mathrm{s}$$

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