Calculator Inputs
Example Data Table
This sample helps users understand the expected input format and typical outputs.
| Case | Initial Velocity | Initial Height | Gravity | Selected Time | Approx. Max Height | Approx. Flight Time |
|---|---|---|---|---|---|---|
| Lab Throw A | 20.0000 m/s | 2.0000 m | 9.8100 m/s² | 1.5000 s | 22.3874 m | 4.1735 s |
| Platform Drop | -5.0000 m/s | 18.0000 m | 9.8100 m/s² | 1.0000 s | 18.0000 m | 1.4846 s |
| Imperial Demo | 55.0000 ft/s | 12.0000 ft | 32.1740 ft/s² | 1.2000 s | 59.0181 ft | 3.7939 s |
Formula Used
Displacement Equation
y(t) = h₀ + ut − ½gt²
Here, h₀ is initial height, u is initial velocity, and g is gravitational acceleration.
Velocity Equation
v(t) = u − gt
This returns the instantaneous vertical velocity at any chosen time.
Time to Peak
tpeak = u / g when u > 0
If the initial velocity is downward or zero, the peak occurs immediately at the start.
Maximum Height
Hmax = h₀ + u² / (2g) when u > 0
This adds the extra rise above the starting point to the initial height.
Flight Time
tflight = (u + √(u² + 2gh₀)) / g
This is the positive root of the vertical position equation when ground level equals zero.
How to Use This Calculator
- Select SI or imperial units.
- Enter initial velocity. Use positive values for upward launch.
- Enter the starting height above the ground reference.
- Set gravity for Earth or any other environment.
- Choose a time for the state calculation.
- Set sample points and output precision.
- Press Calculate Motion to generate results above the form.
- Use the export buttons for CSV and PDF files.
Frequently Asked Questions
1) What does this calculator solve?
It solves one-dimensional vertical projectile motion with constant gravity. It returns height, velocity, peak height, time to peak, total flight time, impact speed, average motion values, a trajectory table, and a plot.
2) What sign convention is used?
Upward is positive. Gravity acts downward, so it subtracts from velocity over time. A negative initial velocity means the object starts by moving downward from the chosen initial height.
3) Can I use imperial units?
Yes. Choose imperial mode to work in feet and feet per second. The gravity box can use Earth’s common value of 32.174 ft/s² or any other constant acceleration you want to test.
4) Why is the selected time sometimes adjusted?
If the chosen time exceeds total flight time, the object has already reached the ground. The calculator then reports the physical state at impact, because motion beyond that point no longer matches the free-flight model.
5) Does this include air resistance?
No. It uses the ideal constant-acceleration model only. That makes it suitable for classroom kinematics, quick checks, and controlled examples where drag is negligible or intentionally ignored.
6) How is maximum height calculated?
When the object launches upward, velocity becomes zero at the top. Using that condition gives the extra rise as u²/(2g). Adding that rise to the starting height gives the maximum height above ground.
7) What does the graph show?
The plot shows height and velocity across time from launch until impact. It helps you see the parabolic height change and the linear velocity change caused by constant gravitational acceleration.
8) When is this calculator most useful?
It is useful for physics homework, lab preparation, demonstrations, engineering checks, and sensitivity testing. Custom gravity also makes it useful for comparing motion across planets or special simulation settings.