8.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{7eedd755-0dfd-4506-b7fd-23b9def4ebc8-24_259_1045_255_456}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}

Figure 4 shows a rough ramp fixed to horizontal ground.\\
The ramp is inclined at angle $\alpha$ to the ground, where $\tan \alpha = \frac { 1 } { 6 }$\\
The point $A$ is on the ground at the bottom of the ramp.\\
The point $B$ is at the top of the ramp.\\
The line $A B$ is a line of greatest slope of the ramp and $A B = 4 \mathrm {~m}$.\\
A particle $P$ of mass 3 kg is projected with speed $U \mathrm {~m} \mathrm {~s} ^ { - 1 }$ from $A$ directly towards $B$.\\
The coefficient of friction between the particle and the ramp is $\frac { 3 } { 4 }$
\begin{enumerate}[label=(\alph*)]
\item Find the work done against friction as $P$ moves from $A$ to $B$.

Given that at the instant $P$ reaches the point $B$, the speed of $P$ is $5 \mathrm {~ms} ^ { - 1 }$
\item use the work-energy principle to find the value of $U$.

The particle leaves the ramp at $B$, and moves freely under gravity until it hits the ground at the point $C$.
\item Find the horizontal distance from $B$ to $C$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2022 Q8 [14]}}