| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2019 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Projectiles |
| Type | Projectile clearing obstacle |
| Difficulty | Standard +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. |
| Spec | 3.03d 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 $\frac{5}{3}d \text{ m s}^{-1}$.
\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]}}