Edexcel M2 2016 January — Question 7 14 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2016
SessionJanuary
Marks14
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicProjectiles
TypeSpeed at specific time or position
DifficultyStandard +0.3 This is a standard M2 projectiles question requiring resolution of velocity components and use of kinematic equations. Part (a) uses the condition at point A to find the launch angle, part (b) applies kinetic energy at maximum height (straightforward since vertical component is zero), and part (c) requires finding when speed equals 6 m/s using the velocity-time relationship. All techniques are routine for M2 students with no novel problem-solving required, making it slightly easier than average.
Spec3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model6.02d Mechanical energy: KE and PE concepts6.02e Calculate KE and PE: using formulae

7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e6d100ff-dd4a-4591-a0a3-81761773045e-13_552_1296_255_317} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} At time \(t = 0\), a particle \(P\) of mass 0.7 kg is projected with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a fixed point \(O\) at an angle \(\theta ^ { \circ }\) to the horizontal. The particle moves freely under gravity. At time \(t = 2\) seconds, \(P\) passes through the point \(A\) with speed \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and is moving downwards at \(45 ^ { \circ }\) to the horizontal, as shown in Figure 4. Find
  1. the value of \(\theta\),
  2. the kinetic energy of \(P\) as it reaches the highest point of its path. For an interval of \(T\) seconds, the speed, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), of \(P\) is such that \(v \leqslant 6\)
  3. Find the value of \(T\).

7.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{e6d100ff-dd4a-4591-a0a3-81761773045e-13_552_1296_255_317}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}

At time $t = 0$, a particle $P$ of mass 0.7 kg is projected with speed $u \mathrm {~m} \mathrm {~s} ^ { - 1 }$ from a fixed point $O$ at an angle $\theta ^ { \circ }$ to the horizontal. The particle moves freely under gravity. At time $t = 2$ seconds, $P$ passes through the point $A$ with speed $6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and is moving downwards at $45 ^ { \circ }$ to the horizontal, as shown in Figure 4.

Find
\begin{enumerate}[label=(\alph*)]
\item the value of $\theta$,
\item the kinetic energy of $P$ as it reaches the highest point of its path.

For an interval of $T$ seconds, the speed, $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$, of $P$ is such that $v \leqslant 6$
\item Find the value of $T$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M2 2016 Q7 [14]}}