5 A particle \(P\) of mass \(m \mathrm {~kg}\) is projected vertically upwards from a point \(O\), with speed \(20 \mathrm {~ms} ^ { - 1 }\), and moves under gravity. There is a resistive force of magnitude \(2 m v \mathrm {~N}\), where \(v \mathrm {~ms} ^ { - 1 }\) is the speed of \(P\) at time \(t \mathrm {~s}\) after projection.

1. Find an expression for \(v\) in terms of \(t\), while \(P\) is moving upwards.
   The displacement of \(P\) from \(O\) is \(x \mathrm {~m}\) at time \(t \mathrm {~s}\).
2. Find an expression for \(x\) in terms of \(t\), while \(P\) is moving upwards.
3. Find, correct to 3 significant figures, the greatest height above \(O\) reached by \(P\).