\begin{enumerate}
  \item \hspace{0pt} [In this question $\mathbf { i }$ and $\mathbf { j }$ are unit vectors, with $\mathbf { i }$ horizontal and $\mathbf { j }$ vertical.]
\end{enumerate}

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{d5f06fe7-4d9c-4009-8931-3ecbc31fa5e5-26_273_889_296_589}
\captionsetup{labelformat=empty}
\caption{Figure 6}
\end{center}
\end{figure}

The fixed points $A$ and $B$ lie on horizontal ground.\\
At time $t = 0$, a particle $P$ is projected from $A$ with velocity $( 4 \mathbf { i } + 7 \mathbf { j } ) \mathrm { ms } ^ { - 1 }$\\
Particle $P$ moves freely under gravity and hits the ground at $B$, as shown in Figure 6 .\\
(a) Find the distance $A B$.

The speed of $P$ is less than $5 \mathrm {~ms} ^ { - 1 }$ for an interval of length $T$ seconds.\\
(b) Find the value of $T$

At the instant when the direction of motion of $P$ is perpendicular to the initial direction of motion of $P$, the particle is $h$ metres above the ground.\\
(c) Find the value of $h$.

\hfill \mbox{\textit{Edexcel M2 2024 Q8 [11]}}