Edexcel M2 2018 October — Question 4 13 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2018
SessionOctober
Marks13
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicProjectiles
TypeSpeed at specific time or position
DifficultyStandard +0.3 This is a standard M2 projectiles question requiring systematic application of kinematic equations. Part (a) uses velocity components at t=2s to find initial conditions (routine reverse-working), part (b) applies standard displacement formulas, and part (c) requires solving a quadratic for times when height equals h. All techniques are textbook exercises with no novel insight required, making it slightly easier than average.
Spec3.02d Constant acceleration: SUVAT formulae3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model

4. At time \(t = 0\) a ball is projected from a fixed point \(A\) on horizontal ground to hit a target. The ball is projected from \(A\) with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\theta ^ { \circ }\) to the horizontal. At time \(t = 2 \mathrm {~s}\) the ball hits the target. At the instant when it hits the target, the ball is travelling downwards at \(30 ^ { \circ }\) below the horizontal with speed \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The ball is modelled as a particle moving freely under gravity and the target is modelled as the point \(T\).
  1. Find
    1. the value of \(\theta\),
    2. the value of \(u\). The height of \(T\) above the ground is \(h\) metres.
  2. Find the value of \(h\).
  3. Find the length of time for which the ball is more than \(h\) metres above the ground during the flight from \(A\) to \(T\).

4. At time $t = 0$ a ball is projected from a fixed point $A$ on horizontal ground to hit a target. The ball is projected from $A$ with speed $u \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle $\theta ^ { \circ }$ to the horizontal. At time $t = 2 \mathrm {~s}$ the ball hits the target. At the instant when it hits the target, the ball is travelling downwards at $30 ^ { \circ }$ below the horizontal with speed $12 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The ball is modelled as a particle moving freely under gravity and the target is modelled as the point $T$.
\begin{enumerate}[label=(\alph*)]
\item Find
\begin{enumerate}[label=(\roman*)]
\item the value of $\theta$,
\item the value of $u$.

The height of $T$ above the ground is $h$ metres.
\end{enumerate}\item Find the value of $h$.
\item Find the length of time for which the ball is more than $h$ metres above the ground during the flight from $A$ to $T$.

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\hfill \mbox{\textit{Edexcel M2 2018 Q4 [13]}}