7.
\begin{figure}[h]
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\caption{Figure 3}
\includegraphics[alt={},max width=\textwidth]{d5250c24-138a-4fe3-91eb-d6f8dca766fb-6_837_1284_468_397}
\end{figure}
A rocket \(R\) of mass 100 kg is projected from a point \(A\) with speed \(80 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of elevation of \(60 ^ { \circ }\), as shown in Fig. 3. The point \(A\) is 20 m vertically above a point \(O\) which is on horizontal ground. The rocket \(R\) moves freely under gravity. At \(B\) the velocity of \(R\) is horizontal. By modelling \(R\) as a particle, find
- the height in m of \(B\) above the ground,
- the time taken for \(R\) to reach \(B\) from \(A\).
When \(R\) is at \(B\), there is an internal explosion and \(R\) breaks into two parts \(P\) and \(Q\) of masses 60 kg and 40 kg respectively. Immediately after the explosion the velocity of \(P\) is \(80 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) horizontally away from \(A\). After the explosion the paths of \(P\) and \(Q\) remain in the plane \(O A B\). Part \(Q\) strikes the ground at \(C\). By modelling \(P\) and \(Q\) as particles,
- show that the speed of \(Q\) immediately after the explosion is \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\),
- find the distance \(O C\).