A child of mass $45 \mathrm{kg}$ travels down a water chute. The child has speed $1 \mathrm{m}{ \mathrm{s}}^{-1}$ at the top of the chute and speed $5{ \mathrm{ms}}^{-1}$ at the bottom of the chute. The length of the water chute is $20 \mathrm{m}$ and the height through which it descends is $4 \mathrm{m}$. Work out the average resistance force that acts.

A boy sits on a sledge at the top of an icy hill. He gently sets the sledge in motion. When he reaches the bottom of the hill he is moving at $10 \mathrm{m}{ \mathrm{s}}^{-1}$. Assuming that friction is negligible, find the height of the hill.

A girl of mass $50 \mathrm{kg}$ sits on a sledge at the top of a grassy hill. She gently sets the sledge in motion. When she reaches the bottom of the hill she is moving at $9.9 \mathrm{m}{ \mathrm{s}}^{-1}$. The hill is $5 \mathrm{m}$ high and the sledge slides $100 \mathrm{m}$ down the hill. Work out the resistance force. (Use $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A girl of mass $50 \mathrm{kg}$ sits on a sledge at the top of a grassy hill. She gently sets the sledge in motion. When she reaches the bottom of the hill she is moving at $9.9 \mathrm{m}{ \mathrm{s}}^{-1}$. The hill is $5 \mathrm{m}$ high and the sledge slides $100 \mathrm{m}$ down the hill.

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A child of mass $40 \mathrm{kg}$ slides down a playground slide. The child starts from rest at the top of the slide, $2 \mathrm{m}$ above the ground. At the bottom of the slide its slope levels off.

Find the child's loss of gravitational potential energy.

There is a constant resistance of $112 \mathrm{N}$ throughout.

A child of mass $40 \mathrm{kg}$ slides down a playground slide. The child starts from rest at the top of the slide, $2 \mathrm{m}$ above the ground. At the bottom of the slide its slope levels off.

Find the distance the child has travelled when she comes to rest.

The slide is inclined at an angle of $30°$ to the horizontal.

A child of mass $40 \mathrm{kg}$ slides down a playground slide. The child starts from rest at the top of the slide, $2 \mathrm{m}$ above the ground. At the bottom of the slide its slope levels off.

Find the distance the child travels on the level part of the slide.

A roller-coaster car has mass $100 \mathrm{kg}$. It carries two passengers, each of mass between $50 \mathrm{kg}$ and $80 \mathrm{kg}$. The car becomes detached from the drive chain and continues to travel along the ride with no drive force and no braking force. The car comes to instantaneous rest at the highest point of the ride and then descends under gravity to reach the lowest point of the ride. The highest point is $12 \mathrm{m}$ vertically above the lowest point. The car travels $100 \mathrm{m}$ along the track while descending through $12 \mathrm{m}$. When the car passes through the lowest point it has speed $15 \mathrm{m}{ \mathrm{s}}^{-1}$.

Show that the average frictional force is less than $20 \mathrm{N}$.