| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2019 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Resultant of three coplanar forces |
| Difficulty | Moderate -0.8 This is a straightforward mechanics question requiring resolution of forces into components using basic trigonometry (sin/cos of standard angles), then vector addition. It's purely procedural with no problem-solving insight needed, making it easier than average, though slightly more involved than pure recall. |
| Spec | 3.03p Resultant forces: using vectors |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \([24\cos 25° - 12\cos 65°]\) | M1 | Resolving in \(x\)-direction |
| \(16.7\ \text{N}\) | A1 | \((16.679...)\) |
| \([30 - 24\sin 25° - 12\sin 65°]\) | M1 | Resolving in \(y\)-direction |
| \(8.98\ \text{N}\) | A1 | \((8.981...)\) |
| 4 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\left[\tan^{-1} \dfrac{8.98...}{16.67...}\right]\) | M1 | Uses trigonometry to find the angle |
| \(28.3°\) (anticlockwise) from \(x\)-direction | A1 | \((28.300...)\) or equivalent |
| 6 |
## Question 2(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $[24\cos 25° - 12\cos 65°]$ | **M1** | Resolving in $x$-direction |
| $16.7\ \text{N}$ | **A1** | $(16.679...)$ |
| $[30 - 24\sin 25° - 12\sin 65°]$ | **M1** | Resolving in $y$-direction |
| $8.98\ \text{N}$ | **A1** | $(8.981...)$ |
| | **4** | |
---
## Question 2(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\left[\tan^{-1} \dfrac{8.98...}{16.67...}\right]$ | **M1** | Uses trigonometry to find the angle |
| $28.3°$ (anticlockwise) from $x$-direction | **A1** | $(28.300...)$ or equivalent |
| | **6** | |2\\
\includegraphics[max width=\textwidth, alt={}, center]{539be201-7bfc-4ba0-8378-c7aec4473ac7-03_577_691_262_724}
Coplanar forces of magnitudes $12 \mathrm {~N} , 24 \mathrm {~N}$ and 30 N act at a point in the directions shown in the diagram.\\
(i) Find the components of the resultant of the three forces in the $x$-direction and in the $y$-direction.
Component in $x$-direction $\_\_\_\_$\\
Component in $y$-direction. $\_\_\_\_$\\
(ii) Hence find the direction of the resultant.\\
\hfill \mbox{\textit{CAIE M1 2019 Q2 [6]}}