M1 January 2008 Q2
2. A firework rocket starts from rest at ground level and moves vertically. In the first 3 s of its motion, the rocket rises 27 m. The rocket is modelled as a particle moving with constant acceleration \(a\) m s\(^{-2}\). Find
(a) the value of \(a\), (2)
(b) the speed of the rocket 3 s after it has left the ground. (2)
After 3 s, the rocket burns out. The motion of the rocket is now modelled as that of a particle moving freely under gravity.
(c) Find the height of the rocket above the ground 5 s after it has left the ground. (4)
| Scheme | Marks |
|---|---|
| \(27 = 0 + \tfrac{1}{2}.a.3^2\ \ \Rightarrow\ \ a = 6\) | M1 A1 |
| (2) |
| Scheme | Marks |
|---|---|
| \(v = 6 \times 3 = 18\) m s\(^{-1}\) | M1 A1 f.t. |
| (2) |
| Scheme | Marks |
|---|---|
| From \(t = 3\) to \(t = 5\), \(s = 18 \times 2 - \tfrac{1}{2} \times 9.8 \times 2^2\) | M1 A1 f.t. |
| Total ht. \(= s + 27 = 43.4\) m, 43 m | M1 A1 |
| (4) | |
| (8 marks) |