1 A small ball \(B\) is projected from a point \(O\) on horizontal ground. The initial velocity of \(B\) has horizontal and vertically upwards components of \(18 \mathrm {~ms} ^ { - 1 }\) and \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively. For the instant 4 s after projection, find the speed and direction of motion of \(B\).
A non-uniform rod \(A B\) of length 0.5 m and weight 8 N is freely hinged to a fixed point at \(A\). The rod makes an angle of \(30 ^ { \circ }\) with the horizontal with \(B\) above the level of \(A\). The rod is held in equilibrium by a force of magnitude 12 N acting in the vertical plane containing the rod at an angle of \(30 ^ { \circ }\) to \(A B\) applied at \(B\) (see diagram). Find the distance of the centre of mass of the rod from \(A\).