6 A particle is projected with speed \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(\theta ^ { \circ }\) above the horizontal. At the instant 4 s after projection the speed of the particle is \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Find \(\theta\).
2. Show that at the instant 4 s after projection the particle is 33.75 m below the level of the point of projection and find the direction of motion at this instant.
   \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{f3a35846-075d-4e03-ba6b-82774ef0e4f8-12_259_609_255_769} \captionsetup{labelformat=empty} \caption{Fig. 1}
   \end{figure} Fig. 1 shows an object made from a uniform wire of length 0.8 m . The object consists of a straight part \(A B\), and a semicircular part \(B C\) such that \(A , B\) and \(C\) lie in the same straight line. The radius of the semicircle is \(r \mathrm {~m}\) and the centre of mass of the object is 0.1 m from line \(A B C\).
3. Show that \(r = 0.2\).
   \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{f3a35846-075d-4e03-ba6b-82774ef0e4f8-13_615_383_260_881} \captionsetup{labelformat=empty} \caption{Fig. 2}
   \end{figure} The object is freely suspended at \(A\) and a horizontal force of magnitude 7 N is applied to the object at \(C\) so that the object is in equilibrium with \(A B C\) vertical (see Fig. 2).
4. Calculate the weight of the object.
   The 7 N force is removed and the object hangs in equilibrium with \(A B C\) at an angle of \(\theta ^ { \circ }\) with the vertical.
5. Find \(\theta\).
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.