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Question Number 75158 by peter frank last updated on 08/Dec/19

Answered by mr W last updated on 08/Dec/19

$$letu=\sqrt{\frac{7ga}{2}}$$$$\frac{1}{2}{mu}^2=\frac{1}{2}{mv}^2+mga(1-\cos \theta )$$$$\Rightarrow v^2=u^2-2ga(1-\cos \theta )$$$$$$$$thestringbecomesslackwhen:$$$$m\frac{v^2}{a}=-mg\cos \theta$$$$\Rightarrow v^2=-ga\cos \theta$$$$\Rightarrow u^2-2ga(1-\cos \theta )=-ga\cos \theta$$$$\Rightarrow \cos \theta =\frac{1}{3}(2-\frac{u^2}{ga})=\frac{1}{3}(2-\frac{7}{2})=-\frac{1}{2}$$$$\Rightarrow \theta =120°$$$$v^2=u^2-2ga(1-\cos \theta )=\frac{7ga}{2}-3ga=\frac{ga}{2}$$$$\Rightarrow v=\sqrt{\frac{ga}{2}}$$

Commented by peter frank last updated on 08/Dec/19

$$thankverymuch$$

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