Oblique impactEdexcel A-Level Further Maths: Mind map

Exam questions on Oblique impact

1. A smooth particle of mass $0.4$ kg moves on a smooth horizontal surface and strikes a fixed smooth vertical wall with speed $10$ m s$^{-1}$. Its direction of motion makes an angle of $60^\circ$ with the wall. The coefficient of restitution between the particle and the wall is $0.5$.
   Find the kinetic energy lost by the particle in the impact.2 marks
2. A smooth ball of mass $0.2$ kg hits a smooth horizontal floor. The unit vectors $\mathbf{i}$ and $\mathbf{j}$ are horizontal and vertically upwards respectively. Immediately before the impact the velocity of the ball is $(6\mathbf{i}-8\mathbf{j})$ m s$^{-1}$. The coefficient of restitution between the ball and the floor is $0.75$.
   Find the speed of the ball immediately after impact, and the angle between its direction of motion and the floor.2 marks
3. Two smooth spheres $A$ and $B$ of equal radii and equal mass $m$ lie on a smooth horizontal surface, with $B$ at rest. $A$ moves with speed $10$ m s$^{-1}$ and strikes $B$. At the instant of impact the direction of motion of $A$ makes an angle $\alpha$ with the line of centres, where $\cos\alpha=0.8$. The coefficient of restitution between the spheres is $0.5$.
   Find the speed of $B$ immediately after the impact.3 marks