\begin{enumerate}
  \item \hspace{0pt} [In this question, the unit vectors $\mathbf { i }$ and $\mathbf { j }$ are in a vertical plane, $\mathbf { i }$ being horizontal and $\mathbf { j }$ being vertically upwards.]
\end{enumerate}

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{e6e37d85-f8de-490a-82a9-8a3c16e2fdd0-20_289_837_347_486}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{center}
\end{figure}

A small ball is projected with velocity $( 6 \mathbf { i } + 12 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$ from a fixed point $A$ on horizontal ground. The ball hits the ground at the point $B$, as shown in Figure 5. The motion of the ball is modelled as a particle moving freely under gravity.\\
(a) Find the distance $A B$.

When the height of the ball above the ground is more than $h$ metres, the speed of the ball is less than $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$\\
(b) Find the smallest possible value of $h$.

When the ball is at the point $C$ on its path, the direction of motion of the ball is perpendicular to the direction of motion of the ball at the instant before it hits the ground at $B$.\\
(c) Find, in terms of $\mathbf { i }$ and $\mathbf { j }$, the velocity of the ball when it is at $C$.\\

\hfill \mbox{\textit{Edexcel M2 2021 Q7 [11]}}