4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{aafbccd2-7ba9-426b-9023-73b556ac3bed-07_574_472_219_744}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
A smooth sphere of radius \(a\) is fixed with a point \(A\) of its surface in contact with a fixed vertical wall. A particle is placed on the highest point of the sphere and is projected towards the wall and perpendicular to the wall with horizontal speed \(\sqrt { \frac { 2 a g } { 5 } }\), as shown in Figure 2.
The particle leaves the surface of the sphere with speed \(V\).
- Show that \(V = \sqrt { \frac { 4 a g } { 5 } }\)
The particle strikes the wall at the point \(X\).
- Find the distance \(A X\).