At the end of a downhill run, a skier of mass $80 \mathrm{kg}$ slides up a rough slope at an angle of $10°$ to the horizontal, to slow down. He arrives at the upward slope with an initial speed of $12 \mathrm{m}{\mathrm{s}}^{-1}.$ The coefficient of friction between the skier and the slope is $0.4.$ Find how far up the slope he comes to rest, and show that he remains at rest there without falling back down the slope.

A book of mass $3 \mathrm{kg}$ is at rest on a rough slope at an angle of $15°$ to the horizontal. It takes a force of $20 \mathrm{N}$ parallel to the slope to break equilibrium and drag it up the slope.

Find the coefficient of friction between the slope and the book.

A book of mass $3 \mathrm{kg}$ is at rest on a rough slope at an angle of $15°$ to the horizontal. It takes a force of $20 \mathrm{N}$ parallel to the slope to break equilibrium and drag it up the slope.

Find the acceleration of the book down the slope if the $20 \mathrm{N}$ force is applied down the slope.

A box of mass $12 \mathrm{kg}$ is at rest on a rough slope at an angle of $18°$ to the horizontal. The coefficient of friction between the slope and the box is $0.4.$

Find the force it takes parallel to the upwards slope to break equilibrium and drag the box up the slope.

A box of mass $12 \mathrm{kg}$ is at rest on a rough slope at an angle of $18°$ to the horizontal. The coefficient of friction between the slope and the box is $0.4.$

If the force were applied down the slope and parallel to it, find the acceleration.