8.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{b4065fe1-55fa-4a01-8ae2-006e0d529c50-24_286_1317_251_317}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\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.
\begin{enumerate}[label=(\alph*)]
\item 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
\item \begin{enumerate}[label=(\roman*)]
\item the value of $w$,
\item the direction of motion of $P$ as it hits the ground at $C$,
\end{enumerate}\item the greatest height of $P$ above the ground as $P$ moves from $A$ to $C$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2019 Q8 [15]}}