Sam and his skateboard have a combined mass of $100 \mathrm{kg}$. He accelerates from $0 \mathrm{m}{ \mathrm{s}}^{-1}$ to $20 \mathrm{m}{ \mathrm{s}}^{-1}$ while descending a hill. The hill is modelled as a slope at an angle of ${\sin }^{-1}0.2$ to the horizontal. The non-gravitational resistance is $200 \mathrm{N}$. The bottom of the hill is $10 \mathrm{m}$ below the top of the hill. Find the increase in the kinetic energy of Sam and his skateboard. (Use $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Sam and his skateboard have a combined mass of $100 \mathrm{kg}$. He accelerates from $0 \mathrm{m}{ \mathrm{s}}^{-1}$ to $20 \mathrm{m}{ \mathrm{s}}^{-1}$ while descending a hill. The hill is modelled as a slope at an angle of ${\sin }^{-1}0.2$ to the horizontal. The non-gravitational resistance is $200 \mathrm{N}$. The bottom of the hill is $10 \mathrm{m}$ below the top of the hill. Find the decrease in the potential energy of Sam and his skateboard. (Use: $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Sam and his skateboard have a combined mass of $100 \mathrm{kg}$. He accelerates from $0 \mathrm{m}{ \mathrm{s}}^{-1}$ to $20 \mathrm{m}{ \mathrm{s}}^{-1}$ while descending a hill. The hill is modelled as a slope at an angle of ${\sin }^{-1}0.2$ to the horizontal. The non-gravitational resistance is $200 \mathrm{N}$. The bottom of the hill is $10 \mathrm{m}$ below the top of the hill. Find the distance that the skateboard travels.

Sam and his skateboard have a combined mass of $100 \mathrm{kg}$. He accelerates from $0 \mathrm{m}{ \mathrm{s}}^{-1}$ to $20 \mathrm{m}{ \mathrm{s}}^{-1}$ while descending a hill. The hill is modelled as a slope at an angle of ${\sin }^{-1}0.2$ to the horizontal. The non-gravitational resistance is $200 \mathrm{N}$. The bottom of the hill is $10 \mathrm{m}$ below the top of the hill. Find the work done against resistance.

Kiera climbs up a ladder to sit at the top of a slide $2 \mathrm{m}$ above the ground. Her potential energy increases by $1280 \mathrm{J}$. Find Kiera's weight.

Kiera climbs up a ladder to sit at the top of a slide $2 \mathrm{m}$ above the ground. Her potential energy increases by $1280 \mathrm{J}$.

Kiera then slides down the slide, starting from rest. The slide is modelled as a slope at an angle $\theta$ to the horizontal. The resistance force is a constant $20 \mathrm{N}$. The work done against resistance by Kiera when she is sliding is $80 \mathrm{J}$. Find the length of the slide. (Use $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Kiera climbs up a ladder to sit at the top of a slide $2 \mathrm{m}$ above the ground. Her potential energy increases by $1280 \mathrm{J}$.

Kiera then slides down the slide, starting from rest. The slide is modelled as a slope at an angle $\theta$ to the horizontal. The resistance force is a constant $20 \mathrm{N}$. The work done against resistance by Kiera when she is sliding is $80 \mathrm{J}$.

Find the value of $\theta$.

Kiera climbs up a ladder to sit at the top of a slide $2 \mathrm{m}$ above the ground. Her potential energy increases by $1280 \mathrm{J}$.

Kiera then slides down the slide, starting from rest. The slide is modelled as a slope at an angle $\theta$ to the horizontal. The resistance force is a constant $20 \mathrm{N}$. The work done against resistance by Kiera when she is sliding is $80 \mathrm{J}$. Find Kiera's speed when she reaches the bottom of the slide. (Use: $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A ramp is inclined at an angle ${\sin }^{-1}0.1$ to the horizontal. A box of mass $40 \mathrm{kg}$ is projected up the ramp with initial speed $5 \mathrm{m}{ \mathrm{s}}^{-1}$. The coefficient of friction between the ramp and the box is $0.05$, and no other resistance forces act.

Find the acceleration of the box, stating its direction. The box comes to rest when it reaches the top of the ramp. (Use: $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)