[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.]

\includegraphics{figure_3}

The point $O$ is a fixed point on a horizontal plane. A ball is projected from $O$ with velocity $(3\mathbf{i} + v\mathbf{j})$ m s$^{-1}$ where $v > 3$. The ball moves freely under gravity and passes through the point $A$ before reaching its maximum height above the horizontal plane, as shown in Figure 3.

The ball passes through $A$ at time $\frac{15}{49}$ s after projection. The initial kinetic energy of the ball is $E$ joules. When the ball is at $A$ it has kinetic energy $\frac{1}{2}E$ joules.

\begin{enumerate}[label=(\alph*)]
\item Find the value of $v$. [8]
\end{enumerate}

At another point $B$ on the path of the ball the kinetic energy is also $\frac{1}{2}E$ joules.

The ball passes through $B$ at time $T$ seconds after projection.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the value of $T$. [3]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2014 Q6 [11]}}