# Toboggan Hill#

Aliyah and their sled, with a combined mass of $${{params.m}}$$ $$\rm{kg}$$, slide $${{params.l}}$$ $$\rm{m}$$ down a hill that makes an angle of $${{params.ang_horiz}}^\circ$$ with the horizontal. They feel a friction force from the snow $$F\_{fr} = {{params.fr}}$$ $$\rm{N}$$ and another force from the wind $$F\_{wind} = {{params.fwind}}$$ $$\rm{N}$$ blowing at $${{params.ang_wind}}^\circ$$ below the horizontal from the top of the hill toward the bottom.

For reference, below is a picture of a sled.

## Part 1#

How much work is done by gravity $$W_g$$ by the time Aliyah gets to the bottom of the hill?

Please enter in a numeric value in $$m{kJ}$$.

## Part 2#

How much work $$W\_{fr}$$ is done by friction by the time Aliyah gets to the bottom of the hill?

Please enter in a numeric value in $$m{kJ}$$.

## Part 3#

How much work $$W_w$$ is done by the wind by the time Aliyah gets to the bottom of the hill?

Please enter in a numeric value in $$m{kJ}$$.

## Part 4#

If Aliyahâ€™s inital speed at the top of the hill is $$v_i = {{params.v_i}}$$ $$\rm{m/s}$$, what is their speed $$v_f$$ at the bottom of the hill?

If you are not able to get an answer for Part 3, you can still get marks for Part 4. Use $$W_w = 10$$ $$\rm{kJ}$$ to continue answering Part 4.

Please enter in a numeric value in $$m{m/s}$$.