Successive direct impactsEdexcel A-Level Further Maths: Mind map

Exam questions on Successive direct impacts

1. A small ball is dropped from rest at a height of $2.5$ m above a smooth horizontal floor. The coefficient of restitution between the ball and the floor is $0.8$. Take $g=9.8$ m s$^{-2}$.
   Find the greatest height reached by the ball after its second bounce.2 marks
2. Two smooth spheres $P$ and $Q$ of equal radii and equal mass $1$ kg lie on a smooth horizontal surface, in a straight line perpendicular to a fixed smooth vertical wall, with $Q$ between $P$ and the wall. $Q$ is at rest and $P$ moves towards $Q$ at $4$ m s$^{-1}$. The coefficient of restitution between $P$ and $Q$ is $0.5$, and between $Q$ and the wall is $\frac23$.
   Explain why $P$ and $Q$ collide a second time.2 marks
3. Three smooth spheres $A$, $B$ and $C$ of equal radii lie in a straight line on a smooth horizontal surface, with $B$ between $A$ and $C$. $A$ has mass $2m$, and $B$ and $C$ each have mass $m$. $B$ and $C$ are at rest. $A$ moves towards $B$ at $6$ m s$^{-1}$. The coefficient of restitution between any two of the spheres is $\frac12$.
   Find the speed of $B$ immediately after the first collision between $A$ and $B$.3 marks