Pre-U Pre-U 9794/3 2020 Specimen — Question 6 6 marks

Exam BoardPre-U
ModulePre-U 9794/3 (Pre-U Mathematics Paper 3)
Year2020
SessionSpecimen
Marks6
TopicVectors Introduction & 2D
TypeResultant of three coplanar forces
DifficultyEasy -1.3 This is a straightforward vector addition problem requiring only basic component addition and then magnitude/angle calculation using Pythagoras and arctangent. Part (a) is trivial arithmetic (12-5, 17+7), and part (b) applies standard formulas with no problem-solving insight needed. Well below average difficulty for A-level mechanics.
Spec1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication

\includegraphics{figure_6} The diagram shows two horizontal forces \(\mathbf{P}\) and \(\mathbf{Q}\) acting at the origin \(O\) of rectangular coordinates \(Oxy\). The components of \(\mathbf{P}\) in the \(x\)- and \(y\)-directions are 12 N and 17 N respectively. The components of \(\mathbf{Q}\) in the \(x\)- and \(y\)-directions are -5 N and 7 N respectively.
  1. Write down the components, in the \(x\)- and \(y\)-directions, of the resultant of \(\mathbf{P}\) and \(\mathbf{Q}\). [2]
  2. Hence, or otherwise, calculate the magnitude of this resultant and the angle the resultant makes with the positive \(x\)-axis. [4]

\includegraphics{figure_6}

The diagram shows two horizontal forces $\mathbf{P}$ and $\mathbf{Q}$ acting at the origin $O$ of rectangular coordinates $Oxy$. The components of $\mathbf{P}$ in the $x$- and $y$-directions are 12 N and 17 N respectively. The components of $\mathbf{Q}$ in the $x$- and $y$-directions are -5 N and 7 N respectively.

\begin{enumerate}[label=(\alph*)]
\item Write down the components, in the $x$- and $y$-directions, of the resultant of $\mathbf{P}$ and $\mathbf{Q}$. [2]

\item Hence, or otherwise, calculate the magnitude of this resultant and the angle the resultant makes with the positive $x$-axis. [4]
\end{enumerate}

\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2020 Q6 [6]}}