| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Collision with vector velocities |
| Difficulty | Moderate -0.3 This is a straightforward momentum conservation problem with one-dimensional vectors. Part (a) requires stating 'particle' (standard modeling), part (b) applies conservation of momentum with simple arithmetic, and part (c) uses impulse-momentum theorem. All steps are routine M1 techniques with no conceptual challenges beyond direct application of standard formulas. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) particle | B1 | |
| (b) cons. of mom. (dir⁰ of bat \(+\)ve): \(1.5(15\hat{i}) + 0.3(-30\hat{j}) = 1.5(5\hat{i}) + 0.3(v\hat{j})\) | M1 A1 | |
| \(6\hat{i} = 0.3v \Rightarrow v = 20\) | M1 A1 | |
| (c) \(F t = \Delta\)mom. i.e. \(F(0.2) = 0.3(20\hat{i} - 30\hat{j})\) | M2 | |
| \(F = 75\hat{i}\) so \(F\) has magnitude 75 N | A1 | (8 marks) |
**(a)** particle | B1 |
**(b)** cons. of mom. (dir⁰ of bat $+$ve): $1.5(15\hat{i}) + 0.3(-30\hat{j}) = 1.5(5\hat{i}) + 0.3(v\hat{j})$ | M1 A1 |
$6\hat{i} = 0.3v \Rightarrow v = 20$ | M1 A1 |
**(c)** $F t = \Delta$mom. i.e. $F(0.2) = 0.3(20\hat{i} - 30\hat{j})$ | M2 |
$F = 75\hat{i}$ so $F$ has magnitude 75 N | A1 | (8 marks)5. A cricket ball of mass 0.3 kg is approaching a batsman at ${ } ^ { - } 30 \mathbf { i } \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The batsman hits the ball with a 1.5 kg bat moving with velocity $15 \mathrm { i } \mathrm { m } \mathrm { s } ^ { - 1 }$. Contact between bat and ball lasts for 0.2 seconds. Immediately after this, bat and ball move with velocities $5 \mathbf { i } \mathrm {~ms} ^ { - 1 }$ and $v \mathbf { i } \mathrm {~ms} ^ { - 1 }$ respectively.
\begin{enumerate}[label=(\alph*)]
\item Suggest a suitable model for the cricket ball.
\item Calculate the value of $v$.
\item Find the magnitude of the force with which the batsman hits the ball.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q5 [8]}}