| Exam Board | WJEC |
|---|---|
| Module | Further Unit 6 (Further Unit 6) |
| Year | 2023 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simple Harmonic Motion |
| Type | Tidal/harbour water level SHM |
| Difficulty | Standard +0.3 This is a standard SHM application question with straightforward setup. Part (a) requires reading amplitude and period from data, (b) is routine SHM equation formulation, (c) involves solving a simple trigonometric equation, and (d) requires differentiation and substitution. All steps are textbook-standard with no novel insight required, making it slightly easier than average. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities1.05o Trigonometric equations: solve in given intervals1.07k Differentiate trig: sin(kx), cos(kx), tan(kx)4.10f Simple harmonic motion: x'' = -omega^2 x |
| Tidal Times | ||||
| High/Low | Time |
| ||
| Low Tide | 5 a.m. | 2 | ||
| High Tide | 11 a.m. | 10 | ||
| Low Tide | 5 p.m. | 2 | ||
| High Tide | 11 p.m. | 10 | ||
3. The vertical motion of a point on the surface of the water in a certain harbour may be modelled as Simple Harmonic Motion about a mean level. The diagram shows that, on a particular day, the depth of water in the harbour at low tide is 2 m and the depth of the water in the harbour at high tide is 10 m . The table below shows the times of high and low tides on this day.\\
\includegraphics[max width=\textwidth, alt={}, center]{d7f600c5-af4a-4708-bfd9-92b37a95c634-4_405_912_621_233}
\begin{center}
\begin{tabular}{ | l | c | c | }
\hline
\multicolumn{3}{|c|}{Tidal Times} \\
\hline
High/Low & Time & \begin{tabular}{ c }
Depth \\
(metres) \\
\end{tabular} \\
\hline
Low Tide & 5 a.m. & 2 \\
\hline
High Tide & 11 a.m. & 10 \\
\hline
Low Tide & 5 p.m. & 2 \\
\hline
High Tide & 11 p.m. & 10 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Write down the period and amplitude of the motion.
\item Let $x \mathrm {~m}$ denote the height of water above mean level $t$ hours after 5a.m. Find an expression for $x$ in terms of $t$.
\item The depth of water must be at least 4 m for boats to safely use the harbour. Determine the earliest time, after low tide at 5 a.m., at which boats can safely leave the harbour and hence find the latest possible time of return before the next low tide.
\item Calculate the rate at which the level of water is falling at 2 p.m.
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 6 2023 Q3 [13]}}