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\includegraphics[max width=\textwidth, alt={}, center]{2bb3c9bb-60f0-440d-a148-b4db3478ca31-3_382_1451_797_347} The diagram shows the vertical cross-section \(A B C D\) of a surface. \(B C\) is a circular arc, and \(A B\) and \(C D\) are tangents to \(B C\) at \(B\) and \(C\) respectively. \(A\) and \(D\) are at the same horizontal level, and \(B\) and \(C\) are at heights 2.7 m and 3.0 m respectively above the level of \(A\) and \(D\). A particle \(P\) of mass 0.2 kg is given a velocity of \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at \(A\), in the direction of \(A B\) (see diagram). The parts of the surface containing \(A B\) and \(B C\) are smooth.

1. Find the decrease in the speed of \(P\) as \(P\) moves along the surface from \(B\) to \(C\). The part of the surface containing \(C D\) exerts a constant frictional force on \(P\), as it moves from \(C\) to \(D\), and \(P\) comes to rest as it reaches \(D\).
2. Find the speed of \(P\) when it is at the mid-point of \(C D\).