7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8e220b8a-46f1-4b9b-88a4-f032c7fbda50-11_501_1018_116_468}
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\caption{Figure 4}
\end{figure}
A particle \(P\) of mass 2 kg is projected up a rough plane with initial speed \(14 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), from a point \(X\) on the plane, as shown in Figure 4. The particle moves up the plane along the line of greatest slope through \(X\) and comes to instantaneous rest at the point \(Y\). The plane is inclined at an angle \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 7 } { 24 }\). The coefficient of friction between the particle and the plane is \(\frac { 1 } { 8 }\).
- Use the work-energy principle to show that \(X Y = 25 \mathrm {~m}\).
After reaching \(Y\), the particle \(P\) slides back down the plane.
- Find the speed of \(P\) as it passes through \(X\).