2. A particle \(P\) of mass \(m\) is above the surface of the Earth at distance \(x\) from the centre of the Earth. The Earth exerts a gravitational force on \(P\). The magnitude of this force is inversely proportional to \(x ^ { 2 }\). At the surface of the Earth the acceleration due to gravity is \(g\). The Earth is modelled as a sphere of radius \(R\).

1. Prove that the magnitude of the gravitational force on \(P\) is \(\frac { m g R ^ { 2 } } { x ^ { 2 } }\). A particle is fired vertically upwards from the surface of the Earth with initial speed \(3 U\). At a height \(R\) above the surface of the Earth the speed of the particle is \(U\).
2. Find \(U\) in terms of \(g\) and \(R\).