6 A particle is projected from a point \(O\) at an angle of \(35 ^ { \circ }\) above the horizontal. At time \(T\) s later the particle passes through a point \(A\) whose horizontal and vertically upward displacements from \(O\) are 8 m and 3 m respectively.

1. By using the equation of the particle's trajectory, or otherwise, find (in either order) the speed of projection of the particle from \(O\) and the value of \(T\).
2. Find the angle between the direction of motion of the particle at \(A\) and the horizontal. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{b9080e9f-2c23-43ce-b171-bd68648dc56b-5_476_895_269_625} \captionsetup{labelformat=empty} \caption{Fig. 1}
   \end{figure} Fig. 1 shows the cross-section of a uniform solid. The cross-section has the shape and dimensions shown. The centre of mass \(C\) of the solid lies in the plane of this cross-section. The distance of \(C\) from \(D E\) is \(y \mathrm {~cm}\).
3. Find the value of \(y\). The solid is placed on a rough plane. The coefficient of friction between the solid and the plane is \(\mu\). The plane is tilted so that \(E F\) lies along a line of greatest slope.
4. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{b9080e9f-2c23-43ce-b171-bd68648dc56b-5_375_431_1366_897} \captionsetup{labelformat=empty} \caption{Fig. 2}
   \end{figure} The solid is placed so that \(F\) is higher up the plane than \(E\) (see Fig. 2). When the angle of inclination is sufficiently great the solid starts to topple (without sliding). Show that \(\mu > \frac { 1 } { 2 }\). [3]
5. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{b9080e9f-2c23-43ce-b171-bd68648dc56b-5_376_428_2069_900} \captionsetup{labelformat=empty} \caption{Fig. 3}
   \end{figure} The solid is now placed so that \(E\) is higher up the plane than \(F\) (see Fig. 3). When the angle of inclination is sufficiently great the solid starts to slide (without toppling). Show that \(\mu < \frac { 5 } { 6 }\). [3]