4 A particle \(P\) is projected from a point \(O\) on horizontal ground with initial speed \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and angle of projection \(30 ^ { \circ }\). At the instant \(t s\) after projection, the horizontal and vertically upwards displacements of \(P\) from \(O\) are \(x \mathrm {~m}\) and \(y \mathrm {~m}\) respectively.

1. Express \(x\) and \(y\) in terms of \(t\) and hence find the equation of the trajectory of \(P\).
   \(P\) is at the same height above the ground at two points which are a horizontal distance apart of 15 m .
2. Calculate this height.
   \includegraphics[max width=\textwidth, alt={}, center]{874622ab-4c75-4a32-bae5-eef780ed0cc0-08_607_1022_255_573} A uniform object is made by joining a solid cone of height 0.8 m and base radius 0.6 m and a cylinder. The cylinder has length 0.4 m and radius 0.5 m . The cylinder has a cylindrical hole of length 0.4 m and radius \(x \mathrm {~m}\) drilled through it along the axis of symmetry. A plane face of the cylinder is attached to the base of the cone so that the object has an axis of symmetry perpendicular to its base and passing through the vertex of the cone. The object is placed with points on the base of the cone and the base of the cylinder in contact with a horizontal surface (see diagram). The object is on the point of toppling.
3. Show that the centre of mass of the object is 0.15 m from the base of the cone.
4. Find \(x\).
   [0pt] [The volume of a cone is \(\frac { 1 } { 3 } \pi r ^ { 2 } h\).]