| Exam Board | CAIE |
|---|---|
| Module | Further Paper 3 (Further Paper 3) |
| Year | 2020 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Impulse and momentum (advanced) |
| Type | Oblique collision of spheres |
| Difficulty | Moderate -0.5 This is a straightforward substitution problem within a larger collision question. Given tan α = 2, students simply substitute into previously derived equations to find a numerical answer. It requires basic algebraic manipulation and trigonometric substitution but no novel problem-solving or conceptual insight beyond standard momentum/impulse techniques already established in earlier parts. |
| Spec | 6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
| Answer | Marks |
|---|---|
| 5 | Where a candidate has misread a number in the question and used that value consistently throughout, provided that number does not alter the difficulty or |
| Answer | Marks |
|---|---|
| 5(a) | Let w be speed of A along line of centres after collision |
| ← mw=−mucosα+musinα | M1 |
| w−0=e(ucosα+usinα) | M1 |
| Answer | Marks |
|---|---|
| sinα( u−eu )=cosα( u+eu ) | M1 |
| Answer | Marks |
|---|---|
| 1−e | A1 |
| Answer | Marks |
|---|---|
| 5(b) | 1 |
| Answer | Marks |
|---|---|
| 3 | B1 |
| Answer | Marks |
|---|---|
| 3 5 5 5 | M1 |
| Answer | Marks |
|---|---|
| Speed = w2 | M1 |
| Answer | Marks |
|---|---|
| 5 5 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 5:
5 | Where a candidate has misread a number in the question and used that value consistently throughout, provided that number does not alter the difficulty or
the method required, award all marks earned and deduct just 1 mark for the misread.
--- 5(a) ---
5(a) | Let w be speed of A along line of centres after collision
← mw=−mucosα+musinα | M1
w−0=e(ucosα+usinα) | M1
Rearrange:
sinα( u−eu )=cosα( u+eu ) | M1
1+e
tanα= . AG
1−e | A1
4
--- 5(b) ---
5(b) | 1
tanα=2e=
3 | B1
1 1 2 u
w= u + =
3 5 5 5 | M1
+( usinα)2
Speed = w2 | M1
u2 4u2
= + =u
5 5 | A1
4
Question | Answer | Marks\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Given that $\tan \alpha = 2$, find the speed of $A$ after the collision. [4]
\end{enumerate}
\hfill \mbox{\textit{CAIE Further Paper 3 2020 Q5 [4]}}