WJEC Unit 2 2022 June — Question 8

Exam BoardWJEC
ModuleUnit 2 (Unit 2)
Year2022
SessionJune
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTravel graphs
TypeMulti-stage motion with all parameters given
DifficultyEasy -1.2 This is a collection of three standard mechanics problems requiring straightforward application of SUVAT equations, Newton's second law with connected particles, and basic vector geometry. Each part involves routine calculations with all parameters given and no problem-solving insight required—significantly easier than average A-level questions.
Spec3.02d Constant acceleration: SUVAT formulae3.03d Newton's second law: 2D vectors3.03k Connected particles: pulleys and equilibrium
An aircraft moves along a straight horizontal runway with a constant acceleration of \(1.5 \mathrm {~ms} ^ { - 2 }\). Points \(A\) and \(B\) lie on the runway. The aircraft passes \(A\) with speed \(4 \mathrm {~ms} ^ { - 1 }\) and its speed at \(B\) must be at least \(78 \mathrm {~ms} ^ { - 1 }\) if it is to take off successfully. a) Find the speed of the aircraft 8 seconds after it passes \(A\).
b) Determine the minimum value of the distance \(A B\) for the aircraft to take off successfully. The diagram below shows an object \(A\), of mass 15 kg , lying on a smooth horizontal surface. It is connected to a box \(B\) by a light inextensible string which passes over a smooth pulley \(P\), fixed at the edge of the surface, so that box \(B\) hangs freely. An object \(C\) lies on the horizontal floor of box \(B\) so that the combined mass of \(B\) and \(C\) is 10 kg . \includegraphics[max width=\textwidth, alt={}, center]{77c62e6d-58e4-42d3-9982-5a8325e8e826-09_661_862_614_598} Initially, the system is held at rest with the string just taut. A horizontal force of magnitude 150 N is then applied to \(A\) in the direction \(P A\) so that box \(B\) is raised.
a) Find the magnitude of the acceleration of \(A\) and the tension in the string.
b) Given that object \(C\) has mass 4 kg , calculate the reaction of the floor of the box on object \(C\).
□
1 In this question, \(\mathbf { i }\) and \(\mathbf { j }\) represent unit vectors due east and due north respectively. Sarah is going for a walk. She leaves her house and walks directly to the shop. She then walks directly from the shop to the park. Relative to her house:
  • the shop has position vector \(\left( - \frac { 2 } { 3 } \mathbf { j } \right) \mathrm { km }\),
  • the park is 2 km away on a bearing of \(060 ^ { \circ }\).
    a) Show that the position vector of the park relative to the house is \(( \sqrt { 3 } \mathbf { i } + \mathbf { j } ) \mathrm { km }\).
    b) Determine the total distance walked by Sarah from her house to the park.
    c) By considering a modelling assumption you have made, explain why the answer you found in part (b) may not be the actual distance that Sarah walked.
An aircraft moves along a straight horizontal runway with a constant acceleration of $1.5 \mathrm {~ms} ^ { - 2 }$. Points $A$ and $B$ lie on the runway. The aircraft passes $A$ with speed $4 \mathrm {~ms} ^ { - 1 }$ and its speed at $B$ must be at least $78 \mathrm {~ms} ^ { - 1 }$ if it is to take off successfully.

a) Find the speed of the aircraft 8 seconds after it passes $A$.\\
b) Determine the minimum value of the distance $A B$ for the aircraft to take off successfully.

The diagram below shows an object $A$, of mass 15 kg , lying on a smooth horizontal surface. It is connected to a box $B$ by a light inextensible string which passes over a smooth pulley $P$, fixed at the edge of the surface, so that box $B$ hangs freely. An object $C$ lies on the horizontal floor of box $B$ so that the combined mass of $B$ and $C$ is 10 kg .\\
\includegraphics[max width=\textwidth, alt={}, center]{77c62e6d-58e4-42d3-9982-5a8325e8e826-09_661_862_614_598}

Initially, the system is held at rest with the string just taut. A horizontal force of magnitude 150 N is then applied to $A$ in the direction $P A$ so that box $B$ is raised.\\
a) Find the magnitude of the acceleration of $A$ and the tension in the string.\\
b) Given that object $C$ has mass 4 kg , calculate the reaction of the floor of the box on object $C$.\\
□\\
1 In this question, $\mathbf { i }$ and $\mathbf { j }$ represent unit vectors due east and due north respectively.

Sarah is going for a walk. She leaves her house and walks directly to the shop. She then walks directly from the shop to the park. Relative to her house:

\begin{itemize}
  \item the shop has position vector $\left( - \frac { 2 } { 3 } \mathbf { j } \right) \mathrm { km }$,
  \item the park is 2 km away on a bearing of $060 ^ { \circ }$.\\
a) Show that the position vector of the park relative to the house is $( \sqrt { 3 } \mathbf { i } + \mathbf { j } ) \mathrm { km }$.\\
b) Determine the total distance walked by Sarah from her house to the park.\\
c) By considering a modelling assumption you have made, explain why the answer you found in part (b) may not be the actual distance that Sarah walked.
\end{itemize}

\hfill \mbox{\textit{WJEC Unit 2 2022 Q8}}
This paper (4 questions)
View full paper
Q2 Q3 Q8 Q11