Chris and his son are skating on an ice rink. Chris skates in a straight line at a speed of $3 \mathrm{m}{ \mathrm{s}}^{-1}$ towards his son, who is stationary on the ice. When they meet Chris lifts his son up and they continue together at a speed of $2 \mathrm{m}{ \mathrm{s}}^{-1}$, still travelling in the same straight line. Chris has mass $80 \mathrm{kg}$. Find the mass of his son.

A ball of mass $0.04 \mathrm{kg}$ is moving at a speed of $3 \mathrm{m}{ \mathrm{s}}^{-1}$ when it hits a stationary ball of mass $0.06 \mathrm{kg}$. After the impact the first ball is stationary. Find the speed of the second ball.

A box of mass $25 \mathrm{kg}$ slides down a slope until it has reached a speed of $5 \mathrm{m}{ \mathrm{s}}^{-1}$ It then travels at $5 \mathrm{m}{ \mathrm{s}}^{-1}$ horizontally across a smooth floor until it bumps into a stationary crate. Immediately after the impact the box reverses its direction and travels at $0.5 \mathrm{m}{ \mathrm{s}}^{-1}$. The crate starts to travel at $2.75 \mathrm{m}{ \mathrm{s}}^{-1}$. Find the mass of the crate.

Two snooker balls are travelling towards one another in a straight line when they make a direct impact. Before the impact the first ball had speed $12 \mathrm{m}{ \mathrm{s}}^{-1}$ and the second ball had speed $8 \mathrm{m}{ \mathrm{s}}^{-1}$. After the impact both balls have reversed their direction and each has speed $10 \mathrm{m}{ \mathrm{s}}^{-1}$. It is claimed that the balls are not both real snooker balls because they have different masses. Find the ratio of the masses of the balls.

Particles $A, B$ and $C$, of masses $0.01 \mathrm{kg},0.06 \mathrm{kg}$ and $0.12 \mathrm{kg}$ respectively, are at rest in a straight line on a smooth horizontal surface, with $B$ between $A$ and $C$. $A$ is given an initial velocity of $4 \mathrm{m}{ \mathrm{s}}^{-1}$ towards $B$. After this impact $A$ rebounds with velocity $2 \mathrm{m}{ \mathrm{s}}^{-1}$ and $B$ goes on to hit $C$. After the second impact $B$ comes to rest. Find the speed of $C$ after the second impact.

Three balls, $A, B$ and $C$, of masses $4 \mathrm{kg},1 \mathrm{kg}$ and $2 \mathrm{kg}$, respectively, are at rest in a straight line on a smooth horizontal surface, with $B$ between $A$ and $C$. $A$ is given an initial velocity of $5 \mathrm{m}{ \mathrm{s}}^{-1}$ towards $B$. When $A$ hits $B$ they coalesce and continue as a single object, $D$, until they collide with $C$. After this collision $C$ has velocity $5 \mathrm{m}{ \mathrm{s}}^{-1}$. Work out the final velocity of $D$.

Jayne is performing in a show on ice. She is pushed onto the ice while sitting on a chair. The chair slides across the ice and Jayne then stands up and moves away from the chair. Jayne has speed $4 \mathrm{m}{ \mathrm{s}}^{-1}$ when she is sitting on the chair and speed $5 \mathrm{m}{ \mathrm{s}}^{-1}$ when she moves away from the chair. Jayne has mass $60 \mathrm{kg}$ and the chair has mass $6 \mathrm{kg}$.

Find the velocity of the chair as Jayne moves away from it.

Jayne is performing in a show on ice. She is pushed onto the ice while sitting on a chair. The chair slides across the ice and Jayne then stands up and moves away from the chair. Jayne has speed $4 \mathrm{m}{ \mathrm{s}}^{-1}$ when she is sitting on the chair and speed $5 \mathrm{m}{ \mathrm{s}}^{-1}$ when she moves away from the chair. Jayne has mass $60 \mathrm{kg}$ and the chair has mass $6 \mathrm{kg}$.

What modelling assumptions have you made?

A bean bag of mass $100 \mathrm{g}$ is thrown at $5 \mathrm{m}{ \mathrm{s}}^{-1}$ at a stationary target. The bean bag sticks to the target and they move of together at $0.1 \mathrm{m}{ \mathrm{s}}^{-1}$. Find the mass of the target.