| Exam Board | CAIE |
|---|---|
| Module | Further Paper 3 (Further Paper 3) |
| Year | 2021 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Perpendicular velocity directions |
| Difficulty | Moderate -0.8 This is a straightforward projectiles question requiring only standard SUVAT equations and basic vector perpendicularity. Parts (a) and (b) are routine bookwork applications, while part (c) is a simple algebraic deduction from the result in (b). The 5 marks total and minimal problem-solving demand place this well below average difficulty for Further Maths. |
| Spec | 1.10h Vectors in kinematics: uniform acceleration in vector form3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| 1(a) | Velocity: →ucosα | B1 |
| ↑usinα−gT | B1 | Allow 10 for g. Must be T. |
| Answer | Marks |
|---|---|
| 1(b) | ucosα sinα |
| Answer | Marks | Guidance |
|---|---|---|
| usinα−gT cosα | M1 FT | Allow missing minus sign on RHS for M1. |
| Answer | Marks |
|---|---|
| gsinα | A1 |
| Answer | Marks |
|---|---|
| 1(c) | u |
| Answer | Marks | Guidance |
|---|---|---|
| g | B1 | AG |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 1:
--- 1(a) ---
1(a) | Velocity: →ucosα | B1
↑usinα−gT | B1 | Allow 10 for g. Must be T.
2
--- 1(b) ---
1(b) | ucosα sinα
=− oe
usinα−gT cosα | M1 FT | Allow missing minus sign on RHS for M1.
FT from (a).
u
T =
gsinα | A1
2
--- 1(c) ---
1(c) | u
sinα<1 giving T >
g | B1 | AG
1
Question | Answer | Marks | GuidanceA particle is projected with speed $u$ at an angle $\alpha$ above the horizontal from a point $O$ on a horizontal plane. The particle moves freely under gravity.
\begin{enumerate}[label=(\alph*)]
\item Write down the horizontal and vertical components of the velocity of the particle at time $T$ after projection. [2]
At time $T$ after projection, the direction of motion of the particle is perpendicular to the direction of projection.
\item Express $T$ in terms of $u$, $g$ and $\alpha$. [2]
\item Deduce that $T > \frac{u}{g}$. [1]
\end{enumerate}
\hfill \mbox{\textit{CAIE Further Paper 3 2021 Q1 [5]}}