| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2017 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Time when specific condition met |
| Difficulty | Standard +0.3 This is a straightforward two-part projectiles question requiring standard kinematic equations. Part (i) is routine (time of flight = 2u/g). Part (ii) requires finding when both particles are moving upward/downward by comparing velocities, which is a standard technique but requires careful tracking of the time offset and some algebraic manipulation. Slightly above average due to the coordination of two particles with different start times, but still a textbook exercise. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02h Motion under gravity: vector form |
| Answer | Marks |
|---|---|
| 4(i) | [12t – ½gt2 = 0] |
| Answer | Marks | Guidance |
|---|---|---|
| [0 = 12 – gT] with t = 2T used | M1 | Using s = ut + ½at2 or equivalent such as |
| Answer | Marks |
|---|---|
| t = 2.4 s | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 4(ii) | Critical point at t = 1.2 | B1 |
| Critical point at t = 2 | B1 | Seen in 4(ii) |
| Answer | Marks |
|---|---|
| 1 < t < 1.2 | B1 |
| Answer | Marks |
|---|---|
| 2 < t < 2.4 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 4:
--- 4(i) ---
4(i) | [12t – ½gt2 = 0]
or
[0 = 12 – gT] with t = 2T used | M1 | Using s = ut + ½at2 or equivalent such as
finding time T to highest point and
doubling.
t = 2.4 s | A1
2
--- 4(ii) ---
4(ii) | Critical point at t = 1.2 | B1 | Seen in 4(ii)
Critical point at t = 2 | B1 | Seen in 4(ii)
Both moving in same direction
1 < t < 1.2 | B1
Both moving in same direction
2 < t < 2.4 | B1
4
Question | Answer | Marks | GuidanceA particle $P$ is projected vertically upwards from horizontal ground with speed 12 m s$^{-1}$.
\begin{enumerate}[label=(\roman*)]
\item Find the time taken for $P$ to return to the ground. [2]
\end{enumerate}
The time in seconds after $P$ is projected is denoted by $t$. When $t = 1$, a second particle $Q$ is projected vertically upwards with speed 10 m s$^{-1}$ from a point which is 5 m above the ground. Particles $P$ and $Q$ move in different vertical lines.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find the set of values of $t$ for which the two particles are moving in the same direction. [4]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2017 Q4 [6]}}