| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2017 |
| Session | June |
| Marks | 9 |
| Topic | Projectiles |
| Type | Horizontal projection from height |
| Difficulty | Moderate -0.8 This is a straightforward two-part projectiles question using standard SUVAT equations with horizontal projection. Part (i) requires finding time from vertical motion then using horizontal distance; part (ii) needs resolving final velocity components. Both are routine textbook exercises requiring only direct application of memorized methods with no problem-solving insight or geometric complexity. |
| Spec | 3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| - \(\therefore | v | = \sqrt{12^2 + (-26)^2} = \sqrt{820} = 28.635\ldots\) M1 |
**Question 7(i)**
**Alternative version 1:**
- Vertical: $-5t^2 = -33.8$ **B1** (Allow absence of both minus signs.)
- $\therefore t = \sqrt{\dfrac{33.8}{5}} = 2.6$ (sec) **B1** (cao)
- Horizontal: $2.6u = 31.2$ **M1**
- $\therefore u = 12$ (ms$^{-1}$) **A1** (FT *their* $t$.)
**Alternative version 2:**
- Horizontal: $ut = 31.2$ **B1**
- $33.8 = 5 \times \dfrac{31.2^2}{u^2}$ **M1** (Eliminate $t$.)
- $\therefore u = \sqrt{\dfrac{5 \times 31.2^2}{33.8}} = 12$ (ms$^{-1}$) **A1**
**Question 7(ii)**
- $v_x = 12$
- Either $v_y = (0) - 10 \times 2.6 = -26$ **B1** (FT *their* $t$. Allow absence of minus sign.)
- Or $v_y = \sqrt{(0^2) + 2 \times 10 \times 33.8} = (-)26$
- $\therefore |v| = \sqrt{12^2 + (-26)^2} = \sqrt{820} = 28.635\ldots$ **M1**
- $\approx 28.6$ (ms$^{-1}$) **A1** (FT *their* $v_y$ and/or $u$.)
- $\theta = \tan^{-1}\left(\dfrac{-26}{12}\right)$ **M1**
- $= -65.2°$ **A1** (Must be negative or have reference to the horizontal, e.g. "below …". FT *their* $v_y$ and/or $u$.)
**Total: 9 marks**7 A building 33.8 m high stands on horizontal ground. A particle is projected horizontally from the top of the building and hits the ground 31.2 m away.\\
(i) Find the initial speed of the particle.\\
(ii) Find the magnitude and direction of the velocity of the particle when it hits the ground.
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2017 Q7 [9]}}