| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2016 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Time when specific condition met |
| Difficulty | Standard +0.3 This is a straightforward projectiles question requiring standard kinematic equations. Part (i) involves substituting t=0.8s into the vertical displacement formula. Part (ii) requires finding the time to maximum height (v=u+at) and comparing with 0.8s. Both parts are routine applications of memorized formulas with minimal problem-solving, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(s = (12\sin30) \times 0.8 - g \times 0.8^2/2\) | M1 | For attempting to find the height above the ground at the position of the post |
| \(H = 1.6 - 0.5 = 1.1\) m | A1 | 1.6 m |
| A1 (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(0 = 12\sin30 - gt\) | M1 | \(t = 0.6\) |
| Time \(= 0.8 - 0.6 = 0.2\) | A1 (2) | AG |
## Question 1:
### Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $s = (12\sin30) \times 0.8 - g \times 0.8^2/2$ | M1 | For attempting to find the height above the ground at the position of the post |
| $H = 1.6 - 0.5 = 1.1$ m | A1 | 1.6 m |
| | A1 (3) | |
### Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $0 = 12\sin30 - gt$ | M1 | $t = 0.6$ |
| Time $= 0.8 - 0.6 = 0.2$ | A1 (2) | **AG** |
---1 A small ball $B$ is projected with speed $12 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle of $30 ^ { \circ }$ above the horizontal from a point $O$ on horizontal ground. At the instant 0.8 s after projection, $B$ is 0.5 m vertically above the top of a vertical post.\\
(i) Calculate the height of the top of the post above the ground.\\
(ii) Show that $B$ is at its greatest height 0.2 s before passing over the post.
\hfill \mbox{\textit{CAIE M2 2016 Q1 [5]}}