3
\includegraphics[max width=\textwidth, alt={}, center]{e30ba526-db21-4904-96dc-c12a1f67c81a-2_397_1303_1790_422} The point \(O\) is 1.2 m below rough horizontal ground \(A B C\). A ball is projected from \(O\) with speed \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(70 ^ { \circ }\) to the horizontal. The ball passes over the point \(A\) after travelling a horizontal distance of 2 m . The ball subsequently bounces once on the ground at \(B\). The ball leaves \(B\) with speed \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and travels a further horizontal distance of 20 m before landing at \(C\) (see diagram).

1. Calculate the height above the level of \(O\) of the ball when it is vertically above \(A\).
2. Calculate the time after the instant of projection when the ball reaches \(B\).
3. Find the angle which the trajectory of the ball makes with the horizontal immediately after it bounces at \(B\).
   \includegraphics[max width=\textwidth, alt={}, center]{e30ba526-db21-4904-96dc-c12a1f67c81a-3_663_695_258_726} A cylinder of height 0.9 m and radius 0.9 m is placed symmetrically on top of a cylinder of height \(h \mathrm {~m}\) and radius \(r \mathrm {~m}\), where \(r < 0.9\), with plane faces in contact and axes in the same vertical line \(A B\), where \(A\) and \(B\) are centres of plane faces of the cylinders (see diagram). Both cylinders are uniform and made of the same material. The lower cylinder is gradually tilted and when the axis of symmetry is inclined at \(45 ^ { \circ }\) to the horizontal the upper cylinder is on the point of toppling without sliding.