Standard +0.8 This is a standard projectile motion problem requiring setup of trajectory equations at two positions and simultaneous equation solving. While it involves algebraic manipulation with the tan⁻¹2 angle (giving component ratios), the approach is methodical rather than requiring novel insight. The 5-mark allocation and straightforward structure place it above average difficulty but not exceptionally challenging for Further Maths students.
A particle \(P\) is projected with speed \(u\text{ms}^{-1}\) at an angle \(\tan^{-1}2\) above the horizontal from a point \(O\) on a horizontal plane and moves freely under gravity. When \(P\) has travelled a distance \(56\text{m}\) horizontally from \(O\), it is at a vertical height \(H\text{m}\) above the plane. When \(P\) has travelled a distance \(84\text{m}\) horizontally from \(O\), it is at a vertical height \(\frac{1}{2}H\text{m}\) above the plane.
Find, in either order, the value of \(u\) and the value of \(H\). [5]
Use equation of trajectory with point (56, H) or 84, H
2
5g 1 5g
H =112− 562 or H =168− 842
Answer
Marks
Guidance
2u2 2 2u2
M1
For one equation with one error.
A1
Both correct.
Eliminate to find u or H
M1
u=35
A1
H = 48
A1
5
Answer
Marks
Guidance
Question
Answer
Marks
Question 1:
1 | 1
Use equation of trajectory with point (56, H) or 84, H
2
5g 1 5g
H =112− 562 or H =168− 842
2u2 2 2u2 | M1 | For one equation with one error.
A1 | Both correct.
Eliminate to find u or H | M1
u=35 | A1
H = 48 | A1
5
Question | Answer | Marks | Guidance
A particle $P$ is projected with speed $u\text{ms}^{-1}$ at an angle $\tan^{-1}2$ above the horizontal from a point $O$ on a horizontal plane and moves freely under gravity. When $P$ has travelled a distance $56\text{m}$ horizontally from $O$, it is at a vertical height $H\text{m}$ above the plane. When $P$ has travelled a distance $84\text{m}$ horizontally from $O$, it is at a vertical height $\frac{1}{2}H\text{m}$ above the plane.
Find, in either order, the value of $u$ and the value of $H$. [5]
\hfill \mbox{\textit{CAIE Further Paper 3 2024 Q1 [5]}}