Free · Physics models
Ideal Downhill Slide and Level Runout
Model acceleration from rest on a straight snowy incline followed by level frictional stopping.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
Loading calculator…
How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
With coefficient 0.1, level runout deceleration is −0.980665 m/s²; a 30-degree slope over two seconds gives downhill speed about 8.11 m/s.
Resolve gravity down the slope and friction uphill; integrate constant acceleration, then use kinetic energy for level runout.
Worked example
Enter these known values and leave the other values blank.
- Type of sled
- Waxed wood on wet snow
- Sliding time
- 2 sec
- Hill length
- 8.108 m
- Hill height
- 4.054 m
- How fast will the sled go at the bottom?
- 29.19 km/h
- Distance to stop
- 33.52 m
- Time to stop
- 8.268 sec
Assumptions and limitations
- The model starts from rest, uses constant kinetic friction and transitions instantly onto level ground. The selected slope must accelerate the sled downhill.
- Friction choices are approximate captured surface scenarios, not measured site properties. Static starting friction, bumps, changing snow and air drag are omitted.
- The speed and distance tiers are numerical context only; they do not determine whether a real slope or runout is safe.
- Clear the unknown numerical field before using a supported inverse; selection controls retain their captured branches.
Common questions
What assumptions matter for this model?
The model starts from rest, uses constant kinetic friction and transitions instantly onto level ground. The selected slope must accelerate the sled downhill.
What does this model leave out?
The speed and distance tiers are numerical context only; they do not determine whether a real slope or runout is safe.
References
Model requirements: The chosen incline must give positive downhill acceleration from rest. Authored accessible explanations preserve each captured diagram mode and its geometric relationships.