| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2016 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Projectile with bounce or impact |
| Difficulty | Standard +0.3 This is a standard two-stage projectile problem with a bounce. Part (i) uses routine SUVAT equations to find time of flight and range. Part (ii) requires finding when speed equals 18 m/s using the speed formula √(u_x² + u_y²) across two flight phases, which is slightly more involved than basic projectile questions but still follows standard M2 techniques without requiring novel insight. |
| Spec | 3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| \(-20\sin 30 = 20\sin 30 - gT\) | M1 | |
| \(T = 2\) s | A1 | |
| \(OA = 34.6\) m | B1 | |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| \(V_v^2 = 18^2 - (20\cos 30)^2\) | M1 | |
| \(V_V = (\pm)\ 4.899\) | A1 | |
| \(4.899 = 20\sin 30 - gt\) | M1 | |
| \(t = 0.51(0)\) s | A1 | |
| \(-4.899 = 8 - gt\) | ||
| \(t = 1.29\) | ||
| \(T = 3.29\) s | A1 | |
| [5] |
## Question 4:
### Part (i):
| Working/Answer | Mark | Guidance |
|---|---|---|
| $-20\sin 30 = 20\sin 30 - gT$ | M1 | |
| $T = 2$ s | A1 | |
| $OA = 34.6$ m | B1 | |
| | [3] | |
### Part (ii):
| Working/Answer | Mark | Guidance |
|---|---|---|
| $V_v^2 = 18^2 - (20\cos 30)^2$ | M1 | |
| $V_V = (\pm)\ 4.899$ | A1 | |
| $4.899 = 20\sin 30 - gt$ | M1 | |
| $t = 0.51(0)$ s | A1 | |
| $-4.899 = 8 - gt$ | | |
| $t = 1.29$ | | |
| $T = 3.29$ s | A1 | |
| | [5] | |
---4 A particle $P$ is projected with speed $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle of $30 ^ { \circ }$ above the horizontal from a point $O$ on horizontal ground. $P$ subsequently bounces when it first strikes the ground at the point $A$.\\
(i) Find the time after projection when $P$ first strikes the ground, and the distance $O A$.
When $P$ bounces at $A$ the horizontal component of the velocity of $P$ is unchanged. The vertical component of velocity is $8 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ immediately after bouncing. $P$ strikes the ground for the second time at $B$ where it remains at rest.\\
(ii) Calculate the first and last times after projection at which the speed of $P$ is $18 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\hfill \mbox{\textit{CAIE M2 2016 Q4 [8]}}