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.
(a) 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 \(t \mathrm{~s}\).
(b) Find an expression for \(x\) in terms of \(t\), while \(P\) is moving upwards.
(c) Find, correct to 3 significant figures, the greatest height above \(O\) reached by \(P\).