| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2013 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Projectile passing through given point |
| Difficulty | Moderate -0.3 This is a standard M1 projectile question requiring straightforward application of kinematic equations with given time, horizontal distance, and vertical height. The three parts systematically guide students through finding horizontal velocity (distance/time), then using vertical motion with SUVAT to find the vertical component, and finally combining components to find V and α. No novel problem-solving or geometric insight required—just routine application of well-practiced techniques. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form3.02d Constant acceleration: SUVAT formulae3.02i Projectile motion: constant acceleration model |
## Question 8:
**Part (a):** Horizontal component of velocity
$v_x = \frac{38.4}{2.4} = 16 \text{ ms}^{-1}$
**Part (b):** Find $V$
Using vertical motion: $s = u_y t - \frac{1}{2}gt^2$
$3 = u_y(2.4) - \frac{1}{2}(9.8)(2.4)^2$
$3 = 2.4u_y - 28.224$
$u_y = \frac{31.224}{2.4} = 13.01 \text{ ms}^{-1}$
$V = \sqrt{16^2 + 13.01^2} = \sqrt{256 + 169.26} \approx 20.6 \text{ ms}^{-1}$
**Part (c):** Find $\alpha$
$\tan\alpha = \frac{13.01}{16}$
$\alpha = \arctan(0.8131) \approx 39.2°$8 A golf ball is hit from a point on a horizontal surface, so that it has an initial velocity $V \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle $\alpha$ above the horizontal. The ball travels through the air and after 2.4 seconds hits a vertical wall at a height of 3 metres. The wall is at a horizontal distance of 38.4 metres from the point where the ball was hit. The path of the ball is shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{ccc1db66-9700-4f22-905e-cc0bdf1fd3c1-18_300_1000_566_520}
Assume that the weight of the ball is the only force that acts on it as it travels through the air.
\begin{enumerate}[label=(\alph*)]
\item Find the horizontal component of the velocity of the ball.
\item $\quad$ Find $V$.
\item $\quad$ Find $\alpha$.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2013 Q8 [10]}}