\includegraphics{figure_3}

Fig. 7 shows the graph of $y = \frac{1}{100}(100 + 15x - x^2)$.

For $0 \leq x < 20$, this graph shows the trajectory of a small stone projected from the point Q where $y$ m is the height of the stone above horizontal ground and $x$ m is the horizontal displacement of the stone from O. The stone hits the ground at the point R.

\begin{enumerate}[label=(\roman*)]
\item Write down the height of Q above the ground. [1]

\item Find the horizontal distance from O of the highest point of the trajectory and show that this point is $1.5625$ m above the ground. [5]

\item Show that the time taken for the stone to fall from its highest point to the ground is $0.565$ seconds, correct to 3 significant figures. [3]

\item Show that the horizontal component of the velocity of the stone is $22.1\text{ms}^{-1}$, correct to 3 significant figures. Deduce the time of flight from Q to R. [5]

\item Calculate the speed at which the stone hits the ground. [4]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI M1  Q3 [18]}}