| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2007 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Deriving trajectory equation |
| Difficulty | Moderate -0.5 This is a standard M2 projectiles question requiring routine application of kinematic equations (x = ut, y = ut - ½gt²) and elimination of parameter t to derive the trajectory equation, followed by substituting y = -25 to find range. The algebra is straightforward and the method is textbook-standard, making it slightly easier than average for A-level. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(x = 7t\) | B1 | |
| \(y = 21t - 4.9t^2\) | M1 | or \(-g/2\) |
| A1 | ||
| \(y = 21 \cdot \frac{x}{7} - 4.9\frac{x^2}{49}\) | M1 | |
| \(y = 3x - \frac{x^2}{10}\) | A1 5 | AG |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(-25 = 3x - \frac{x^2}{10}\) (must be \(-25\)) | M1 | or method for total time \((5.26)\) |
| solving quadratic | M1 | or \(7\times\) total time |
| \(36.8\) m | A1 3 |
## Question 4(i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $x = 7t$ | B1 | |
| $y = 21t - 4.9t^2$ | M1 | **or** $-g/2$ |
| | A1 | |
| $y = 21 \cdot \frac{x}{7} - 4.9\frac{x^2}{49}$ | M1 | |
| $y = 3x - \frac{x^2}{10}$ | A1 **5** | **AG** |
## Question 4(ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $-25 = 3x - \frac{x^2}{10}$ (must be $-25$) | M1 | **or** method for total time $(5.26)$ |
| solving quadratic | M1 | **or** $7\times$ total time |
| $36.8$ m | A1 **3** | |
---4 A ball is projected from a point $O$ on the edge of a vertical cliff. The horizontal and vertically upward components of the initial velocity are $7 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $21 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ respectively. At time $t$ seconds after projection the ball is at the point $( x , y )$ referred to horizontal and vertically upward axes through $O$. Air resistance may be neglected.\\
(i) Express $x$ and $y$ in terms of $t$, and hence show that $y = 3 x - \frac { 1 } { 10 } x ^ { 2 }$.
The ball hits the sea at a point which is 25 m below the level of $O$.\\
(ii) Find the horizontal distance between the cliff and the point where the ball hits the sea.
\hfill \mbox{\textit{OCR M2 2007 Q4 [8]}}