8 A particle, \(P\), of mass 5 kg is placed at the point \(A\) on a rough plane which is inclined at \(30 ^ { \circ }\) to the horizontal. The points \(Q\) and \(R\) are also on the surface of the inclined plane, with \(Q R = 15\) metres. The point \(A\) is between \(Q\) and \(R\) so that \(A Q = 4\) metres and \(A R = 11\) metres. The three points \(Q , A\) and \(R\) are on a line of greatest slope of the plane.
\includegraphics[max width=\textwidth, alt={}, center]{7c2c50e0-4976-4301-9898-61b2760a2aee-20_391_882_676_587} The particle is attached to two light elastic strings, \(P Q\) and \(P R\).
One of the strings, \(P Q\), has natural length 4 metres and modulus of elasticity 160 N , the other string, \(P R\), has natural length 6 metres and modulus of elasticity 120 N . The particle is released from rest at the point \(A\).
The coefficient of friction between the particle and the plane is 0.4 .
Find the distance of the particle from \(Q\) when it is next at rest.
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