| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2014 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | SUVAT in 2D & Gravity |
| Type | Two particles: same start time, different heights |
| Difficulty | Moderate -0.3 This is a straightforward two-particle SUVAT problem requiring standard application of kinematic equations with gravity. Students must find the time of flight for P using v = u + at (giving t = 2.24s), then use this to find h and V for Q using standard equations. All steps are routine with no conceptual challenges beyond recognizing both particles have the same time of flight. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02h Motion under gravity: vector form |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \([-11 = 11 - 10t]\) | M1 | For using \(v = u - gt\) (or equivalent method) to find duration of motion |
| Time after projection is 2.2 seconds | A1 | 2 marks total |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \(h = 0 + \frac{1}{2}g \times 2.2^2 = 24.2\) | B1\(\checkmark\) | |
| \(V = 0 + g \times 2.2 = 22\) | B1\(\checkmark\) | 2 marks total |
## Question 1:
### Part (i):
| Working | Mark | Guidance |
|---------|------|----------|
| $[-11 = 11 - 10t]$ | M1 | For using $v = u - gt$ (or equivalent method) to find duration of motion |
| Time after projection is 2.2 seconds | A1 | 2 marks total |
### Part (ii):
| Working | Mark | Guidance |
|---------|------|----------|
| $h = 0 + \frac{1}{2}g \times 2.2^2 = 24.2$ | B1$\checkmark$ | |
| $V = 0 + g \times 2.2 = 22$ | B1$\checkmark$ | 2 marks total |
---1 A particle $P$ is projected vertically upwards with speed $11 \mathrm {~ms} ^ { - 1 }$ from a point on horizontal ground. At the same instant a particle $Q$ is released from rest at a point $h \mathrm {~m}$ above the ground. $P$ and $Q$ hit the ground at the same instant, when $Q$ has speed $V \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(i) Find the time after projection at which $P$ hits the ground.\\
(ii) Hence find the values of $h$ and $V$.
\hfill \mbox{\textit{CAIE M1 2014 Q1 [4]}}