A tennis ball is projected with velocity vector $(30\mathbf{i} - 14\mathbf{j})$ ms$^{-1}$ from a point $P$ which is at a height of $2.4$ m vertically above a horizontal tennis court. The ball then passes over a net of height $0.9$ m, before hitting the ground after $\frac{4}{7}$ s.

The unit vectors $\mathbf{i}$ and $\mathbf{j}$ are horizontal and vertical respectively. The origin $O$ lies on the ground directly below the point $P$. The base of the net is $x$ m from $O$.

\includegraphics{figure_10}

\begin{enumerate}[label=(\alph*)]
\item Find the speed of the ball when it first hits the ground, giving your answer correct to one decimal place. [3]

\item After $\frac{2}{5}$ s, the ball is directly above the net.
\begin{enumerate}[label=(\roman*)]
\item Find the position vector of the ball after $\frac{2}{5}$ s.

\item Hence determine the value of $x$ and show that the ball clears the net by approximately $16$ cm. [4]
\end{enumerate}

\item In fact, the ball clears the net by only $4$ cm.
\begin{enumerate}[label=(\roman*)]
\item Explain why the observed value is different from the value calculated in (b)(ii).

\item Suggest a possible improvement to this model. [2]
\end{enumerate}
\end{enumerate}

\hfill \mbox{\textit{WJEC Unit 4 2019 Q10 [9]}}