1 A small ball \(B\) is projected with speed \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(60 ^ { \circ }\) to the horizontal from a point on horizontal ground. Find the time after projection when the speed of \(B\) is \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for the second time.
[0pt] [4]
\includegraphics[max width=\textwidth, alt={}, center]{ef38fda2-230b-431a-8064-82e4a3bff393-04_620_668_255_742} A uniform object is made by attaching the base of a solid hemisphere to the base of a solid cone so that the object has an axis of symmetry. The base of the cone has radius 0.3 m , and the hemisphere has radius 0.2 m . The object is placed on a horizontal plane with a point \(A\) on the curved surface of the hemisphere and a point \(B\) on the circumference of the cone in contact with the plane (see diagram).

1. Given that the object is on the point of toppling about \(B\), find the distance of the centre of mass of the object from the base of the cone.
2. Given instead that the object is on the point of toppling about \(A\), calculate the height of the cone.
   [0pt] [The volume of a cone is \(\frac { 1 } { 3 } \pi r ^ { 2 } h\). The volume of a hemisphere is \(\frac { 2 } { 3 } \pi r ^ { 3 }\).]