5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{266c4f52-f35f-459c-9184-836b0f3baf5b-16_255_1242_301_360}
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\caption{Figure 2}
\end{figure}
A smooth straight ramp is fixed to horizontal ground. The ramp has length 8 m and is inclined at \(30 ^ { \circ }\) to the ground, as shown in Figure 2. A particle \(P\) of mass 0.7 kg is projected from a point \(A\) at the bottom of the ramp, up a line of greatest slope of the ramp, with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\). As \(P\) reaches the point \(B\) at the top of the ramp, \(P\) has speed \(4.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- By considering energy, find the value of \(u\).
After leaving the ramp at \(B\), the particle \(P\) moves freely under gravity until it hits the ground at a point \(C\). Immediately before hitting the ground at \(C\), particle \(P\) is moving at \(\theta ^ { \circ }\) below the horizontal with speed \(w \mathrm {~ms} ^ { - 1 }\).
Find
- the value of \(w\),
- the value of \(\theta\),
- the horizontal distance from \(B\) to \(C\).