8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b4065fe1-55fa-4a01-8ae2-006e0d529c50-24_286_1317_251_317}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
A rough ramp \(A B\) is fixed to horizontal ground at \(A\). The ramp is inclined at \(20 ^ { \circ }\) to the ground. The line \(A B\) is a line of greatest slope of the ramp and \(A B = 6 \mathrm {~m}\). The point \(B\) is at the top of the ramp, as shown in Figure 3. A particle \(P\) of mass 3 kg is projected with speed \(15 \mathrm {~ms} ^ { - 1 }\) from \(A\) towards \(B\). At the instant \(P\) reaches the point \(B\) the speed of \(P\) is \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The force due to friction is modelled as a constant force of magnitude \(F\) newtons.
- Use the work-energy principle to find the value of \(F\).
After leaving the ramp at \(B\), the particle \(P\) moves freely under gravity until it hits the horizontal ground at the point \(C\). The speed of \(P\) as it hits the ground at \(C\) is \(w \mathrm {~ms} ^ { - 1 }\).
Find
- the value of \(w\),
- the direction of motion of \(P\) as it hits the ground at \(C\),
- the greatest height of \(P\) above the ground as \(P\) moves from \(A\) to \(C\).