Coefficient of restitution and collisionsAQA A-Level Further Maths: Mind map

Exam questions on Coefficient of restitution and collisions

1. A ball is moving at $8$ m s⁻¹ directly towards a fixed smooth vertical wall. It hits the wall and rebounds directly with speed $5$ m s⁻¹.
   After rebounding, the ball hits a second fixed smooth wall, parallel to the first and made of the same material, directly. Find the speed of the ball after it rebounds from the second wall.2 marks
2. Two smooth spheres $A$ and $B$, each of mass $m$, move in the same direction along a straight line on a smooth horizontal surface. $A$ is moving at $5$ m s⁻¹ and $B$ is ahead of it, moving at $1$ m s⁻¹. The spheres collide directly. The coefficient of restitution between them is $0.5$.
   Find, in terms of $m$, the kinetic energy lost in the collision.2 marks
3. A particle $P$ of mass $2m$, moving at $4u$, collides directly with a particle $Q$ of mass $m$ moving at $u$ in the opposite direction on a smooth horizontal surface. The coefficient of restitution between $P$ and $Q$ is $\frac15$.
   Find the speeds of $P$ and $Q$ after the collision.3 marks