AQA M1 — Question 5

Exam BoardAQA
ModuleM1 (Mechanics 1)
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicProjectiles
TypeBasic trajectory calculations
DifficultyModerate -0.8 This is a straightforward projectiles question requiring only standard formulas and basic algebraic manipulation. Part (a) uses vertical motion equation with given components, (b) applies horizontal distance formula, (c) uses Pythagoras on velocity components, and (d) requires recognizing minimum speed occurs at maximum height (horizontal component only). All parts are routine applications of memorized techniques with no problem-solving insight needed.
Spec3.02d Constant acceleration: SUVAT formulae3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model

5 A golf ball is projected from a point \(O\) with initial velocity \(V\) at an angle \(\alpha\) to the horizontal. The ball first hits the ground at a point \(A\) which is at the same horizontal level as \(O\), as shown in the diagram. \includegraphics[max width=\textwidth, alt={}, center]{6151e6ab-30af-4d1c-ab4a-e7dbad170cbf-005_227_602_484_735} It is given that \(V \cos \alpha = 6 u\) and \(V \sin \alpha = 2.5 u\).
  1. Show that the time taken for the ball to travel from \(O\) to \(A\) is \(\frac { 5 u } { g }\).
  2. Find, in terms of \(g\) and \(u\), the distance \(O A\).
  3. Find \(V\), in terms of \(u\).
  4. State, in terms of \(u\), the least speed of the ball during its flight from \(O\) to \(A\).

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5 A golf ball is projected from a point $O$ with initial velocity $V$ at an angle $\alpha$ to the horizontal. The ball first hits the ground at a point $A$ which is at the same horizontal level as $O$, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{6151e6ab-30af-4d1c-ab4a-e7dbad170cbf-005_227_602_484_735}

It is given that $V \cos \alpha = 6 u$ and $V \sin \alpha = 2.5 u$.
\begin{enumerate}[label=(\alph*)]
\item Show that the time taken for the ball to travel from $O$ to $A$ is $\frac { 5 u } { g }$.
\item Find, in terms of $g$ and $u$, the distance $O A$.
\item Find $V$, in terms of $u$.
\item State, in terms of $u$, the least speed of the ball during its flight from $O$ to $A$.
\end{enumerate}

\hfill \mbox{\textit{AQA M1  Q5}}