\includegraphics{figure_7}

A particle $P$ is projected from a point $O$ with initial speed $10 \text{ m s}^{-1}$ at an angle of $45°$ above the horizontal. $P$ subsequently passes through the point $A$ which is at an angle of elevation of $30°$ from $O$ (see diagram). At time $t \text{ s}$ after projection the horizontal and vertically upward displacements of $P$ from $O$ are $x \text{ m}$ and $y \text{ m}$ respectively.

\begin{enumerate}[label=(\roman*)]
\item Write down expressions for $x$ and $y$ in terms of $t$, and hence obtain the equation of the trajectory of $P$. [3]
\item Calculate the value of $x$ when $P$ is at $A$. [3]
\item Find the angle the trajectory makes with the horizontal when $P$ is at $A$. [4]
\end{enumerate}

\hfill \mbox{\textit{CAIE M2 2010 Q7 [10]}}