6.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{1dea68fe-7916-41ed-894e-6b48f8d989bb-20_273_1058_246_443}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}

A rough straight ramp is fixed to horizontal ground. The ramp has length 15 m and is inclined at an angle $\alpha$ to the ground, where $\tan \alpha = \frac { 5 } { 12 }$. The line $A B$ is a line of greatest slope of the ramp, where $A$ is at the bottom of the ramp, and $B$ is at the top of the ramp, as shown in Figure 3.

A particle $P$ of mass 6 kg is projected up the ramp with speed $14 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ from $A$ in a straight line towards $B$. The coefficient of friction between $P$ and the ramp is 0.25
\begin{enumerate}[label=(\alph*)]
\item Find the work done against friction as $P$ moves from $A$ to $B$.

At the instant $P$ reaches $B$, the speed of $P$ is $v \mathrm {~ms} ^ { - 1 }$. After leaving the ramp at $B$, the particle $P$ moves freely under gravity until it hits the horizontal ground at the point $C$. Immediately before hitting the ground at $C$, the speed of $P$ is $w \mathrm {~ms} ^ { - 1 }$
\item Use the work-energy principle to find
\begin{enumerate}[label=(\roman*)]
\item the value of $v$,
\item the value of $w$.\\

\begin{center}

\end{center}

\includegraphics[max width=\textwidth, alt={}, center]{1dea68fe-7916-41ed-894e-6b48f8d989bb-23_86_49_2617_1884}
\end{enumerate}\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2020 Q6 [10]}}