A girl of mass $35 \mathrm{kg}$ jumps from a rock onto the beach below. Her initial vertical speed is $0 \mathrm{m}{ \mathrm{s}}^{-1}$ and she falls $2.45 \mathrm{m}$ under gravity.

Find the speed of the girl when she lands on the beach.

A girl of mass $35 \mathrm{kg}$ jumps from a rock onto the beach below. Her initial vertical speed is $0 \mathrm{m}{ \mathrm{s}}^{-1}$ and she falls $2.45 \mathrm{m}$ under gravity.

Find the downward momentum of the girl just before she lands on the beach.

A book of mass $2 \mathrm{kg}$ falls from a window ledge and drops $1.8 \mathrm{m}$ to the ground. It falls freely under gravity.

Find the speed of the book just before it hits the ground.

A book of mass $2 \mathrm{kg}$ falls from a window ledge and drops $1.8 \mathrm{m}$ to the ground. It falls freely under gravity.

Find the downward momentum of the book just before it hits the ground.

A ball of mass$0.2 \mathrm{kg}$ falls $1.25 \mathrm{m}$ vertically downwards to the ground, starting from rest. It hits the ground and rebounds. The downwards momentum of the ball changes by $1.6 \mathrm{N} \mathrm{s}$ in the bounce.

What height does the ball reach after this bounce?

A ball of mass$0.2 \mathrm{kg}$ falls $1.25 \mathrm{m}$ vertically downwards to the ground, starting from rest. It hits the ground and rebounds. The downwards momentum of the ball changes by $1.6 \mathrm{N} \mathrm{s}$ in the bounce.

By considering the modelling assumptions, explain why the height might be less than this.

A ball bearing of mass $25 \mathrm{g}$ is thrown vertically upwards, and is caught on the way back down. The ball bearing has an initial speed of $3 \mathrm{m}{ \mathrm{s}}^{-1}$ upwards and is travelling at $2 \mathrm{m}{ \mathrm{s}}^{-1}$ when it is caught. Find the change in its momentum.

A hockey ball of mass $0.2 \mathrm{kg}$ is hit so that it has an initial speed of $8 \mathrm{m}{ \mathrm{s}}^{-1}$. The ball travels in a horizontal straight line with acceleration $a \mathrm{m}{ \mathrm{s}}^{-2}$ given by $a=-0.5-kt$ where $t$ is the time in seconds, measured from when the ball was hit. After $2 \mathrm{s}$ the ball has travelled $\frac{41}{3} \mathrm{m}$. It is then intercepted by a player from the other team. This player hits the ball so that its direction of travel is reversed and its speed is now $5 \mathrm{m}{ \mathrm{s}}^{-1}$. Show that when the ball is hit by the second player its momentum changes in magnitude by $2 \mathrm{N} \mathrm{s}$.

Particle $A$ of mass $5 \mathrm{kg}$ is moving at a speed of $2 \mathrm{m}{ \mathrm{s}}^{-1}$ when it hits a stationary particle, $B$, of mass $2 \mathrm{kg}$. After the impact, particle $A$ has speed $0 \mathrm{m}{ \mathrm{s}}^{-1}$ and particle $B$ has speed $v \mathrm{m}{ \mathrm{s}}^{-1}$. The loss in momentum for particle $A$ equals the gain in momentum for particle $B$. Find the value of $v$.