7 A particle \(P\) is projected with speed \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(60 ^ { \circ }\) above the horizontal from a point \(O\). At the instant 1 s later a particle \(Q\) is projected from \(O\) with the same initial speed at an angle of \(45 ^ { \circ }\) above the horizontal. The two particles collide when \(Q\) has been in motion for \(t \mathrm {~s}\).

1. Show that \(t = 2.414\), correct to 3 decimal places.
2. Find the value of \(V\). The collision occurs after \(P\) has passed through the highest point of its trajectory.
3. Calculate the vertical distance of \(P\) below its greatest height when \(P\) and \(Q\) collide. \footnotetext{Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity.
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