OCR H240/03 2019 June — Question 8 10 marks

Exam BoardOCR
ModuleH240/03 (Pure Mathematics and Mechanics)
Year2019
SessionJune
Marks10
PaperDownload PDF ↗
TopicProjectiles
TypeProjectile clearing obstacle
DifficultyStandard +0.3 This is a standard projectile motion question requiring routine application of SUVAT equations and Pythagoras' theorem. Parts (a)-(c) involve straightforward substitution into kinematic formulas, while part (d) requires solving a quadratic equation from the speed condition. The multi-step nature and 10 marks elevate it slightly above average, but no novel insight is needed—just systematic application of standard A-level mechanics techniques.
Spec3.03d Newton's second law: 2D vectors3.03f Weight: W=mg3.03k Connected particles: pulleys and equilibrium3.03v Motion on rough surface: including inclined planes

A particle \(P\) projected from a point \(O\) on horizontal ground hits the ground after \(2.4\) seconds. The horizontal component of the initial velocity of \(P\) is \(\frac{5}{3}d \text{ m s}^{-1}\).
  1. Find, in terms of \(d\), the horizontal distance of \(P\) from \(O\) when it hits the ground. [1]
  2. Find the vertical component of the initial velocity of \(P\). [2]
\(P\) just clears a vertical wall which is situated at a horizontal distance \(d\) m from \(O\).
  1. Find the height of the wall. [3]
The speed of \(P\) as it passes over the wall is \(16 \text{ m s}^{-1}\).
  1. Find the value of \(d\) correct to \(3\) significant figures. [4]

A particle $P$ projected from a point $O$ on horizontal ground hits the ground after $2.4$ seconds.

The horizontal component of the initial velocity of $P$ is $\frac{5}{3}d \text{ m s}^{-1}$.

\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $d$, the horizontal distance of $P$ from $O$ when it hits the ground. [1]

\item Find the vertical component of the initial velocity of $P$. [2]
\end{enumerate}

$P$ just clears a vertical wall which is situated at a horizontal distance $d$ m from $O$.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumii}{2}
\item Find the height of the wall. [3]
\end{enumerate}

The speed of $P$ as it passes over the wall is $16 \text{ m s}^{-1}$.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumii}{3}
\item Find the value of $d$ correct to $3$ significant figures. [4]
\end{enumerate}

\hfill \mbox{\textit{OCR H240/03 2019 Q8 [10]}}