How someone help me out on A level Further Math, 9231, summer 06, paper 2, number...

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...11 ii, mechanics? Thanks.? A particle, P, is suspended from a fixed point, O, by a light inextensible string of length, a. When hanging at rest under gravity at A it is given a horizontal velocity, u. The particle moves freely in a vertical circle and the string slackens when OP makes an angle of 60degrees with the upward vertical.
i) Find u in terms of a and g. [6]
ii) Verify that, when the string next becomes taut, the particle is at A. [6]
iii) What is the speed of the particle just before it reaches A? [2]
 
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