M4 June 2008 Q2
2. Two small smooth spheres \(A\) and \(B\) have equal radii. The mass of \(A\) is \(2m\) kg and the mass of \(B\) is \(m\) kg. The spheres are moving on a smooth horizontal plane and they collide. Immediately before the collision the velocity of \(A\) is \((2\mathbf{i} - 2\mathbf{j})\) m s\(^{-1}\) and the velocity of \(B\) is \((-3\mathbf{i} - \mathbf{j})\) m s\(^{-1}\). Immediately after the collision the velocity of \(A\) is \((\mathbf{i} - 3\mathbf{j})\) m s\(^{-1}\).
Find the speed of \(B\) immediately after the collision. (5)
| Scheme | Marks |
|---|---|
| \(2m(2\mathbf{i} - 2\mathbf{j}) + m(-3\mathbf{i} - \mathbf{j}) = 2m(\mathbf{i} - 3\mathbf{j}) + m\mathbf{v}\) | M1 A1 |
| \((\mathbf{i} - 5\mathbf{j}) = (2\mathbf{i} - 6\mathbf{j}) + \mathbf{v}\) | |
| \((-\mathbf{i} + \mathbf{j}) = \mathbf{v}\) | A1 |
| \(|\mathbf{v}| = \sqrt{(-1)^2 + 1^2} = \sqrt{2}\) m s\(^{-1}\) cwo | DM1 A1 |
| (5 marks) |