| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Basic trajectory calculations |
| Difficulty | Moderate -0.8 This is a straightforward projectile motion question requiring standard SUVAT equations applied to vertical and horizontal components. All three parts follow directly from basic formulas with given angle, time of flight, and g=10 m/s². No problem-solving insight needed—pure routine calculation. |
| Spec | 3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(V\sin40 - (1.8/2)g = 0\) | M1 | Or \(0 = (V\sin40)\times1.8 - g\times1.8^2/2\) |
| \(V = 14(.0)\) ms\(^{-1}\) | A1 [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \((14\sin40)^2 = 2gh\) | M1 | Or \(h = (V\sin40)\times0.9 - g\times0.9^2/2\) |
| \(h = 4.05\) m | A1 [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(d = (14\cos40)\times1.8\) | M1 | Or \(d = V^2\sin80/g\) |
| \(d = 19.3\) m | A1 [2] [6] |
## Question 4:
### Part (i)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $V\sin40 - (1.8/2)g = 0$ | M1 | Or $0 = (V\sin40)\times1.8 - g\times1.8^2/2$ |
| $V = 14(.0)$ ms$^{-1}$ | A1 [2] | |
### Part (ii)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $(14\sin40)^2 = 2gh$ | M1 | Or $h = (V\sin40)\times0.9 - g\times0.9^2/2$ |
| $h = 4.05$ m | A1 [2] | |
### Part (iii)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $d = (14\cos40)\times1.8$ | M1 | Or $d = V^2\sin80/g$ |
| $d = 19.3$ m | A1 [2] [6] | |
---4 A ball $B$ is projected from a point $O$ on horizontal ground at an angle of $40 ^ { \circ }$ above the horizontal. $B$ hits the ground 1.8 s after the instant of projection. Calculate\\
(i) the speed of projection of $B$,\\
(ii) the greatest height of $B$,\\
(iii) the distance from $O$ of the point at which $B$ hits the ground.
\hfill \mbox{\textit{CAIE M2 2013 Q4 [6]}}