| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Modelling assumptions and limitations |
| Difficulty | Standard +0.3 Parts (a) and (b) are standard SUVAT applications requiring direct formula substitution. Part (c) requires setting up equations for two objects and finding when they meet, which is a common M1 problem-solving task but involves more algebraic manipulation. Part (d) tests conceptual understanding. Overall slightly easier than average due to straightforward setup and standard techniques. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02h Motion under gravity: vector form |
| Answer | Marks |
|---|---|
| \(s = 122.5\), \(u = 0\), \(a = g\) use \(s = ut + \frac{1}{4}at^2\) | M1 |
| \(122.5 = 4.9t^2 \Rightarrow t = 5\) | M1 A1 |
| Answer | Marks |
|---|---|
| \(v^2 = u^2 + 2as = 0 + 2g(122.5)\) | M1 |
| \(v = 49\) ms\(^{-1}\) | A1 |
| Answer | Marks |
|---|---|
| \(s = u(t - 2) + \frac{1}{4}(t - 2)^2\) | M1 |
| Jim must hit before \(t = 5\) i.e. \(122.5 = 3u + 4.9(3)^2\) | M2 A1 |
| \(3u = 78.4 \Rightarrow u = 26.1\) ms\(^{-1}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| e.g. \(u\) larger as tennis ball would have experienced more air resistance due to greater speed / large surface area for mass | B2 | (12) |
**Part (a):**
$s = 122.5$, $u = 0$, $a = g$ use $s = ut + \frac{1}{4}at^2$ | M1 |
$122.5 = 4.9t^2 \Rightarrow t = 5$ | M1 A1 |
**Part (b):**
$v^2 = u^2 + 2as = 0 + 2g(122.5)$ | M1 |
$v = 49$ ms$^{-1}$ | A1 |
**Part (c):**
$s = u(t - 2) + \frac{1}{4}(t - 2)^2$ | M1 |
Jim must hit before $t = 5$ i.e. $122.5 = 3u + 4.9(3)^2$ | M2 A1 |
$3u = 78.4 \Rightarrow u = 26.1$ ms$^{-1}$ | A1 |
**Part (d):**
e.g. $u$ larger as tennis ball would have experienced more air resistance due to greater speed / large surface area for mass | B2 | (12)
---Whilst looking over the edge of a vertical cliff, 122.5 metres in height, Jim dislodges a stone. The stone falls freely from rest towards the sea below.
Ignoring the effect of air resistance,
\begin{enumerate}[label=(\alph*)]
\item calculate the time it would take for the stone to reach the sea, [3 marks]
\item find the speed with which the stone would hit the water. [2 marks]
\end{enumerate}
Two seconds after the stone begins to fall, Jim throws a tennis ball downwards at the stone. The tennis ball's initial speed is $u$ m s$^{-1}$ and it hits the stone before they both reach the water.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the minimum value of $u$. [5 marks]
\item If you had taken air resistance into account in your calculations, what effect would this have had on your answer to part (c)? Explain your answer. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q7 [12]}}