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\includegraphics[max width=\textwidth, alt={}, center]{b2cd1b68-523f-40c3-8a51-acb2b55ae8c0-10_289_1191_269_475} The diagram shows a smooth track which lies in a vertical plane. The section \(A B\) is a quarter circle of radius 1.8 m with centre \(O\). The section \(B C\) is a horizontal straight line of length 7.0 m and \(O B\) is perpendicular to \(B C\). The section \(C F E\) is a straight line inclined at an angle of \(\theta ^ { \circ }\) above the horizontal. A particle \(P\) of mass 0.5 kg is released from rest at \(A\). Particle \(P\) collides with a particle \(Q\) of mass 0.1 kg which is at rest at \(B\). Immediately after the collision, the speed of \(P\) is \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the direction \(B C\). You should assume that \(P\) is moving horizontally when it collides with \(Q\).

1. Show that the speed of \(Q\) immediately after the collision is \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
   When \(Q\) reaches \(C\), it collides with a particle \(R\) of mass 0.4 kg which is at rest at \(C\). The two particles coalesce. The combined particle comes instantaneously to rest at \(F\). You should assume that there is no instantaneous change in speed as the combined particle leaves \(C\), nor when it passes through \(C\) again as it returns down the slope.
2. Given that the distance \(C F\) is 0.4 m , find the value of \(\theta\).
3. Find the distance from \(B\) at which \(P\) collides with the combined particle.
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.