Momentum, impulse and collisions requiring resolvingAQA A-Level Further Maths: Mind map

Exam questions on Momentum, impulse and collisions requiring resolving

1. A smooth ball of mass $0.2$ kg hits a fixed smooth vertical wall with speed $10$ m s⁻¹. Its direction of motion before the impact makes an angle of $60^\circ$ with the wall. The coefficient of restitution between the ball and the wall is $0.5$.
   Find the speed of the ball immediately after the impact.2 marks
2. A smooth ball of mass $0.3$ kg moves on a smooth horizontal floor with velocity $(8\mathbf{i}-6\mathbf{j})$ m s⁻¹ and hits a fixed smooth vertical wall that is parallel to the vector $\mathbf{i}$. The coefficient of restitution between the ball and the wall is $0.75$. Here $\mathbf{i}$ and $\mathbf{j}$ are perpendicular horizontal unit vectors.
   Find the angle through which the direction of motion of the ball is deflected by the impact.2 marks
3. A smooth sphere of mass $0.5$ kg hits a fixed smooth vertical wall with speed $20$ m s⁻¹. Before the impact its direction of motion makes an angle $\alpha$ with the wall, where $\tan\alpha=\frac43$. The coefficient of restitution between the sphere and the wall is $\frac34$.
   Find the speed of the sphere immediately after the impact.3 marks