M1 January 2011 Q2
2. A ball is thrown vertically upwards with speed \(u\) m s\(^{-1}\) from a point \(P\) at height \(h\) metres above the ground. The ball hits the ground 0.75 s later. The speed of the ball immediately before it hits the ground is 6.45 m s\(^{-1}\). The ball is modelled as a particle.
(a) Show that \(u = 0.9\) (3)
(b) Find the height above \(P\) to which the ball rises before it starts to fall towards the ground again. (2)
(c) Find the value of \(h\). (3)
| Scheme | Marks |
|---|---|
| \(-6.45 = u - 9.8 \times 0.75\) | M1 A1 |
| \(0.9 = u\) ** | A1 |
| (3) |
| Scheme | Marks |
|---|---|
| \(0 = 0.81 - 2 \times 9.8 \times s\) | M1 |
| \(s = 0.041\) or 0.0413 | A1 |
| (2) |
| Scheme | Marks |
|---|---|
| \(h = -0.9 \times 0.75 + 4.9 \times 0.75^2\) | M1 A1 |
| \(h = 2.1\) or 2.08 | A1 |
| (3) | |
| (8 marks) |