| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Basic trajectory calculations |
| Difficulty | Moderate -0.3 This is a standard M1 projectile motion question with vertical motion under gravity. All parts use routine SUVAT equations with straightforward application: finding maximum height, final speed, and time of flight. The multi-part structure and need to account for initial height (2.5m) adds slight complexity, but these are textbook exercises requiring no novel insight or problem-solving beyond direct formula application. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| (a) speed (m s\(^{-1}\)) 24 graph with V-shape with minimum at \(t = O'\) | B3 | |
| (b) at max. height, \(v = 0\); use \(v^2 = u^2 + 2as\) with \(a = -9.8\), \(u = 24\) \(0 = 576 - 19.6s \ldots s = 29.387\ldots\) start value 2.5 m, so max. height \(= 31.89 \text{ m}\) (nearest cm) | M1 M1 A1 A1 | |
| (c) use \(v^2 = u^2 + 2as\) with \(a = -9.8\), \(u = 24\) and \(s = -2.5\) (up is +ve) \(v^2 = 576 + 49 = 625\) so \(v = \pm 25\) i.e. speed \(= 25 \text{ ms}^{-1}\) downwards | M1 M1 A1 A1 | |
| (d) use \(v = u + at\) with \(v = 25\), \(u = 24\) a \(= 9.8\) (down is +ve) \(25 = 24 + 9.8t \therefore t = 5\) | M1 M1 A1 | (14) |
**(a)** speed (m s$^{-1}$) 24 graph with V-shape with minimum at $t = O'$ | B3 |
**(b)** at max. height, $v = 0$; use $v^2 = u^2 + 2as$ with $a = -9.8$, $u = 24$ $0 = 576 - 19.6s \ldots s = 29.387\ldots$ start value 2.5 m, so max. height $= 31.89 \text{ m}$ (nearest cm) | M1 M1 A1 A1 |
**(c)** use $v^2 = u^2 + 2as$ with $a = -9.8$, $u = 24$ and $s = -2.5$ (up is +ve) $v^2 = 576 + 49 = 625$ so $v = \pm 25$ i.e. speed $= 25 \text{ ms}^{-1}$ downwards | M1 M1 A1 A1 |
**(d)** use $v = u + at$ with $v = 25$, $u = 24$ a $= 9.8$ (down is +ve) $25 = 24 + 9.8t \therefore t = 5$ | M1 M1 A1 | (14)
---Anila is practising catching tennis balls. She uses a mobile computer-controlled machine which fires tennis balls vertically upwards from a height of 2.5 metres above the ground. Once it has fired a ball, the machine is programmed to move position rapidly to allow Anila time to get into a suitable position to catch the ball.
The machine fires a ball at 24 ms$^{-1}$ vertically upwards and Anila catches the ball just before it touches the ground.
\begin{enumerate}[label=(\alph*)]
\item Draw a speed-time graph for the motion of the ball from the time it is fired by the machine to the instant before Anila catches it. [3 marks]
\item Find, to the nearest centimetre, the maximum height which the ball reaches above the ground. [4 marks]
\item Calculate the speed at which the ball is travelling when Anila catches it. [4 marks]
\item Calculate the length of time that the ball is in the air. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q6 [14]}}