| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2014 |
| Session | November |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Distance from velocity-time graph |
| Difficulty | Moderate -0.5 This is a standard SUVAT kinematics problem involving projectile motion with two parts: proving a relationship between angles and finding a specific angle value. While it requires understanding of projectile motion and trigonometry, it follows a well-established template for A-level mechanics questions with straightforward application of standard equations. The proof and calculation are routine for M1 level, making it slightly easier than average. |
| Spec | 3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \([W\cos\alpha + 7 \times 0.6 = 8]\) | M1 | For resolving forces acting at \(O\) vertically |
| \(W\cos\alpha = 3.8\) (cwo) | A1 | AG |
| \(W\sin\alpha = 5.6\) | B1 | [3 marks] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| M1 | For using \(W^2 = (W\sin\alpha)^2 + (W\cos\alpha)^2\) or \(\tan\alpha = (W\sin\alpha \div W\cos\alpha)\) | |
| \(W = 6.77\) or \(\alpha = 55.8\) | A1 | |
| \(\alpha = 55.8\) or \(W = 6.77\) | B1 | [3 marks] |
## Question 3:
### Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $[W\cos\alpha + 7 \times 0.6 = 8]$ | M1 | For resolving forces acting at $O$ vertically |
| $W\cos\alpha = 3.8$ (cwo) | A1 | AG |
| $W\sin\alpha = 5.6$ | B1 | **[3 marks]** |
### Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| | M1 | For using $W^2 = (W\sin\alpha)^2 + (W\cos\alpha)^2$ **or** $\tan\alpha = (W\sin\alpha \div W\cos\alpha)$ |
| $W = 6.77$ or $\alpha = 55.8$ | A1 | |
| $\alpha = 55.8$ or $W = 6.77$ | B1 | **[3 marks]** |
---3\\
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Each of three light inextensible strings has a particle attached to one of its ends. The other ends of the strings are tied together at a point $O$. Two of the strings pass over fixed smooth pegs and the particles hang freely in equilibrium. The weights of the particles and the angles between the sloping parts of the strings and the vertical are as shown in the diagram. It is given that $\sin \beta = 0.8$ and $\cos \beta = 0.6$.\\
(i) Show that $W \cos \alpha = 3.8$ and find the value of $W \sin \alpha$.\\
(ii) Hence find the values of $W$ and $\alpha$.
\hfill \mbox{\textit{CAIE M1 2014 Q3}}