WJEC Further Unit 6 2024 June — Question 4

Exam BoardWJEC
ModuleFurther Unit 6 (Further Unit 6)
Year2024
SessionJune
PaperDownload PDF ↗
TopicSimple Harmonic Motion
TypeMaximum speed in SHM
DifficultyStandard +0.3 This is a standard Further Maths SHM question requiring application of the standard formulas (v² = ω²(a² - x²) and a = -ω²x) to find period and maximum speed, followed by solving a trigonometric equation for timing. All steps are routine applications of well-known SHM results with no novel insight required, making it slightly easier than average.
Spec4.10f Simple harmonic motion: x'' = -omega^2 x4.10g Damped oscillations: model and interpret
  1. The diagram below shows part of a game at a funfair that consists of a target moving along a straight horizontal line \(A B\). The centre of the target may be modelled as a particle moving with Simple Harmonic Motion about centre \(O\), where \(O\) is the midpoint of \(A B\). \includegraphics[max width=\textwidth, alt={}, center]{36112cfa-20c4-4ba8-b972-6b7b44e5182f-14_245_1145_525_452}
When the target is at a distance of 84 cm from \(O\), its speed is \(52 \mathrm { cms } ^ { - 1 }\) and the magnitude of its acceleration is \(1344 \mathrm { cms } ^ { - 2 }\).
  1. Show that the period of the motion is \(\frac { \pi } { 2 } \mathrm {~s}\).
    (b) Determine the maximum speed of the target.Examiner
  2. During a game, players fire a ball at the target. A timer is started when the target is at \(A\). Players must wait for the target to complete at least one full cycle before firing. Given that the target is hit when it is at a distance of 67 cm from \(O\), calculate the two earliest possible times taken to hit the target.
    \section*{PLEASE DO NOT WRITE ON THIS PAGE}
Question 4:
AnswerMarks
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Question 4:
4 | 13
\begin{enumerate}
  \item The diagram below shows part of a game at a funfair that consists of a target moving along a straight horizontal line $A B$. The centre of the target may be modelled as a particle moving with Simple Harmonic Motion about centre $O$, where $O$ is the midpoint of $A B$.\\
\includegraphics[max width=\textwidth, alt={}, center]{36112cfa-20c4-4ba8-b972-6b7b44e5182f-14_245_1145_525_452}
\end{enumerate}

When the target is at a distance of 84 cm from $O$, its speed is $52 \mathrm { cms } ^ { - 1 }$ and the magnitude of its acceleration is $1344 \mathrm { cms } ^ { - 2 }$.\\
(a) Show that the period of the motion is $\frac { \pi } { 2 } \mathrm {~s}$.\\

\begin{center}
\begin{tabular}{|l|l|}
\hline
(b) Determine the maximum speed of the target. & Examiner \\
\hline
\end{tabular}
\end{center}

(c) During a game, players fire a ball at the target. A timer is started when the target is at $A$. Players must wait for the target to complete at least one full cycle before firing. Given that the target is hit when it is at a distance of 67 cm from $O$, calculate the two earliest possible times taken to hit the target.\\

\section*{PLEASE DO NOT WRITE ON THIS PAGE}

\hfill \mbox{\textit{WJEC Further Unit 6 2024 Q4}}
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