4. A particle \(P\) of mass \(m\) is fired vertically upwards from a point on the surface of the Earth and initially moves in a straight line directly away from the centre of the Earth. When \(P\) is at a distance \(x\) from the centre of the Earth, the gravitational force exerted by the Earth on \(P\) is directed towards the centre of the Earth and has a magnitude which 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 fixed sphere of radius \(R\).

1. Show that the magnitude of the gravitational force acting on \(P\) is \(\frac { m g R ^ { 2 } } { x ^ { 2 } }\) The particle was fired with initial speed \(U\) and the greatest height above the surface of the Earth reached by \(P\) is \(\frac { R } { 20 }\) Given that air resistance can be ignored,
2. find \(U\) in terms of \(g\) and \(R\).