| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 14 |
| Topic | Projectiles |
| Type | Projectile clearing obstacle |
| Difficulty | Standard +0.3 This is a standard projectile motion question requiring routine application of SUVAT equations and trajectory formulas. Part (a) involves finding maximum height and vertical position at a given horizontal distance—both textbook exercises. Part (b) requires solving a quadratic equation from the trajectory equation. Parts (c) and (d) are standard modelling commentary. The calculations are straightforward with no novel problem-solving required, making this slightly easier than average. |
| Spec | 3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model |
A girl is practising netball. She throws the ball from a height of 1.5 m above horizontal ground and aims to get the ball through a hoop. The hoop is 2.5 m vertically above the ground and is 6 m horizontally from the point of projection.
The situation is modelled as follows.
\begin{itemize}
\item The initial velocity of the ball has magnitude $U$ m s$^{-1}$.
\item The angle of projection is $40°$.
\item The ball is modelled as a particle.
\item The hoop is modelled as a point.
\end{itemize}
This is shown on the diagram below.
\includegraphics{figure_12}
\begin{enumerate}[label=(\alph*)]
\item For $U = 10$, find
\begin{enumerate}[label=(\roman*)]
\item the greatest height above the ground reached by the ball [5]
\item the distance between the ball and the hoop when the ball is vertically above the hoop. [4]
\end{enumerate}
\item Calculate the value of $U$ which allows her to hit the hoop. [3]
\item How appropriate is this model for predicting the path of the ball when it is thrown by the girl? [1]
\item Suggest one improvement that might be made to this model. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2017 Q12 [14]}}