6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f7a2bf93-a7fc-43c5-b317-109320f633ba-10_611_748_246_534}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
[In this question, the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are in a vertical plane, \(\mathbf { i }\) being horizontal and \(\mathbf { j }\) being vertical.]
A particle \(P\) is projected from the point \(A\) which has position vector 47.5j metres with respect to a fixed origin \(O\). The velocity of projection of \(P\) is \(( 2 u \mathbf { i } + 5 u \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). The particle moves freely under gravity passing through the point \(B\) with position vector \(30 \mathbf { i }\) metres, as shown in Figure 3.
- Show that the time taken for \(P\) to move from \(A\) to \(B\) is 5 s .
- Find the value of \(u\).
- Find the speed of \(P\) at \(B\).