Edexcel M2 2016 June — Question 6 13 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2016
SessionJune
Marks13
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicProjectiles
TypeVector form projectile motion
DifficultyStandard +0.3 This is a standard M2 projectile motion question using vector notation. Part (a) requires setting up position equations and solving a quadratic, which is routine. Parts (b)(i) and (b)(ii) involve finding velocity components and calculating speed/angle using standard formulas. All techniques are textbook exercises with no novel problem-solving required, making it slightly easier than average.
Spec1.10c Magnitude and direction: of vectors3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model

6. [In this question, \(\mathbf { i }\) is a horizontal unit vector and \(\mathbf { j }\) is an upward vertical unit vector.] A particle \(P\) is projected from a fixed origin \(O\) with velocity ( \(3 \mathbf { i } + 4 \mathbf { j }\) ) \(\mathrm { m } \mathrm { s } ^ { - 1 }\). The particle moves freely under gravity and passes through the point \(A\) with position vector \(\lambda ( \mathbf { i } - \mathbf { j } ) \mathrm { m }\), where \(\lambda\) is a positive constant.
  1. Find the value of \(\lambda\).
  2. Find
    1. the speed of \(P\) at the instant when it passes through \(A\),
    2. the direction of motion of \(P\) at the instant when it passes through \(A\).
      HMAV SIHI NITIIIUM ION OC
      VILV SIHI NI JAHM ION OC
      VJ4V SIHI NI JIIYM ION OC

6. [In this question, $\mathbf { i }$ is a horizontal unit vector and $\mathbf { j }$ is an upward vertical unit vector.]

A particle $P$ is projected from a fixed origin $O$ with velocity ( $3 \mathbf { i } + 4 \mathbf { j }$ ) $\mathrm { m } \mathrm { s } ^ { - 1 }$. The particle moves freely under gravity and passes through the point $A$ with position vector $\lambda ( \mathbf { i } - \mathbf { j } ) \mathrm { m }$, where $\lambda$ is a positive constant.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $\lambda$.
\item Find
\begin{enumerate}[label=(\roman*)]
\item the speed of $P$ at the instant when it passes through $A$,
\item the direction of motion of $P$ at the instant when it passes through $A$.\\

HMAV SIHI NITIIIUM ION OC\\
VILV SIHI NI JAHM ION OC\\
VJ4V SIHI NI JIIYM ION OC

\begin{center}

\end{center}
\end{enumerate}\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2016 Q6 [13]}}