A diver jumps from a $10 \mathrm{m}$ board above a swimming pool. The diver has an initial velocity of $u \mathrm{m}{ \mathrm{s}}^{-1}$ upwards. The horizontal component of the diver's path is negligible. A constant resistance of $0.5 \mathrm{N}{ \mathrm{kg}}^{-1}$ acts on the diver. Find an expression for the height of the diver above the pool at the highest point of her dive. (Use: $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A golf ball of mass $45.9 \mathrm{g}$ is hit from a tee with speed $50{ \mathrm{ms}}^{-1}$. The ball lands in a pond that is $5 \mathrm{m}$ lower than the tee. When the ball lands in the pond it has travelled along a curved path of length $160 \mathrm{m}$. The resistance acting on the ball has magnitude $0.3 \mathrm{N}$.

Find the speed of the ball just before it hits the water.

The water immediately absorbs $8 \mathrm{J}$ of energy from the ball. The ball then sinks vertically downwards to reach the bottom of the pond. The resistance acting on the ball has magnitude $3 \mathrm{N}$ and the ball just comes to rest as it reaches the bottom of the pond.

A golf ball of mass $45.9 \mathrm{g}$ is hit from a tee with speed $50{ \mathrm{ms}}^{-1}$. The ball lands in a pond that is $5 \mathrm{m}$ lower than the tee. When the ball lands in the pond it has travelled along a curved path of length $160 \mathrm{m}$. The resistance acting on the ball has magnitude $0.3 \mathrm{N}$.

Find the depth of the pond.

A golf ball of mass $45.9 \mathrm{g}$ is hit from a tee with speed $180 \mathrm{km}{ \mathrm{h}}^{-1}$. The ball rises to a height of $20 \mathrm{m}$, having travelled along a curved path of length $61.875 \mathrm{m}$. At the highest point of its path the ball is travelling at $144 \mathrm{km}{ \mathrm{h}}^{-1}$.

Find the magnitude of the average resistance force acting on the golf ball.

The ball travels a further $105.8 \mathrm{m}$ along a curved path to land on the green. The green is $4 \mathrm{m}$ lower than the tee. The average resistance remains unchanged.

A golf ball of mass $45.9 \mathrm{g}$ is hit from a tee with speed $180 \mathrm{km}{ \mathrm{h}}^{-1}$. The ball rises to a height of $20 \mathrm{m}$, having travelled along a curved path of length $61.875 \mathrm{m}$. At the highest point of its path the ball is travelling at $144 \mathrm{km}{ \mathrm{h}}^{-1}$.

Find the speed of the ball just before it lands on the green.

The ball is travelling vertically when it lands on the green, where it is immediately brought to rest.

A golf ball of mass $45.9 \mathrm{g}$ is hit from a tee with speed $180 \mathrm{km}{ \mathrm{h}}^{-1}$. The ball rises to a height of $20 \mathrm{m}$, having travelled along a curved path of length $61.875 \mathrm{m}$. At the highest point of its path the ball is travelling at $144 \mathrm{km}{ \mathrm{h}}^{-1}$.

Show that the energy absorbed by the green is $28.1 \mathrm{J}$.

Two particles, $A$ and $B$, are connected by a light inextensible string. Particle $A$ has mass $2 \mathrm{kg}$ and particle $B$ has mass $5 \mathrm{kg}$. The string passes over a pulley and hangs vertically with particle $A$ and particle $B$ on each side of the pulley. The pulley, however, is not smooth and $10 \mathrm{J}$ of energy is dissipated for each rotation of the pulley. The system is released from rest, and the particles reach a speed of $0.2 \mathrm{m}{ \mathrm{s}}^{-1}$ after each moving $1.6 \mathrm{m}$.

Work out how many rotations the pulley has made.

Two particles, $A$ and $B$, are connected by a light inextensible string. Particle $A$ has mass $2 \mathrm{kg}$ and particle $B$ has mass $5 \mathrm{kg}$. The string passes over a pulley and hangs vertically with particle $A$ and particle $B$ on each side of the pulley. The pulley, however, is not smooth and $10 \mathrm{J}$ of energy is dissipated for each rotation of the pulley. The system is released from rest, and the particles reach a speed of $0.2 \mathrm{m}{ \mathrm{s}}^{-1}$ after each moving $1.6 \mathrm{m}$.

If the string passes over the pulley without slipping, work out the radius of the pulley.

A woman of weight $54 \mathrm{N}$ skis from point $X$ to point $Y$. The distance from point $X$ to point $Y$ is $16.2 \mathrm{m}$. Point $Y$ is $3 \mathrm{m}$ lower than point $X$. At point $X$ she has speed $1 \mathrm{m}{ \mathrm{s}}^{-1}$ and at point $Y$ she has speed $7 \mathrm{m}{ \mathrm{s}}^{-1}$.

Use the work-energy principle to work out the average resistance force that acts on the woman.