3. A particle, \(P\), is projected vertically upwards with speed \(U\) from a fixed point \(O\). At the instant when \(P\) reaches its greatest height \(H\) above \(O\), a second particle, \(Q\), is projected with speed \(\frac { 1 } { 2 } U\) vertically upwards from \(O\).

1. Find \(H\) in terms of \(U\) and \(g\).
2. Find, in terms of \(U\) and \(g\), the time between the instant when \(Q\) is projected and the instant when the two particles collide.
3. Find where the two particles collide. DO NOT WRITEIN THIS AREA
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