Calculator Inputs
Example Data Table
| Case | Speed (m/s) | Angle (°) | Takeoff Height (m) | Landing Height (m) | Distance (m) | Flight Time (s) | Peak Height (m) |
|---|---|---|---|---|---|---|---|
| School training | 9.4 | 21 | 1.00 | 0.00 | 7.992 | 0.911 | 1.578 |
| Competition trial | 10.2 | 19 | 1.05 | 0.00 | 8.794 | 0.912 | 1.612 |
| Raised landing zone | 8.8 | 24 | 0.95 | 0.10 | 7.383 | 0.918 | 1.603 |
Formula Used
This calculator models the jump as projectile motion. It assumes a clean takeoff, constant gravity, and no air resistance.
Given:
v = takeoff speed
θ = takeoff angle
g = gravity
h₀ = takeoff height
hₗ = landing height
Horizontal speed:
vx = v × cos(θ)
Vertical speed:
vy = v × sin(θ)
Flight time:
t = [vy + √(vy² + 2g(h₀ - hₗ))] / g
Horizontal distance:
R = vx × t
Maximum rise above takeoff:
H = vy² / (2g)
Peak height above ground:
Hpeak = h₀ + H
This output is useful for classroom physics, sports analysis, and quick planning studies. Official competition results still depend on board accuracy, body position, and landing technique.
How to Use This Calculator
- Enter the athlete's takeoff speed and choose the correct speed unit.
- Provide the takeoff angle in degrees.
- Enter takeoff and landing heights using the same distance unit.
- Set gravity, or keep 9.81 m/s² for standard Earth conditions.
- Press Calculate Long Jump to display the result above the form.
- Review the tiles, motion summary, and trajectory graph.
- Use the CSV or PDF buttons to save the current report.
FAQs
1) What does this calculator estimate?
It estimates horizontal jump distance from takeoff speed, launch angle, takeoff height, landing height, and gravity. It also reports airtime, peak height, landing speed, and the plotted path.
2) Is this suitable for official competition scoring?
No. Official long jump distance is measured from the takeoff board to the nearest mark in the sand. This tool is a physics model, not a judging system.
3) Why does the angle matter so much?
Angle changes how speed splits into horizontal and vertical components. A low angle keeps more forward speed, while a higher angle increases airtime. The best range depends on the full input set.
4) Can I use feet or miles per hour?
Yes. The calculator accepts m/s, km/h, mph, and ft/s for speed. It also accepts meters, centimeters, and feet for height and displayed distance.
5) Does it include air resistance?
No. The model assumes ideal projectile motion with constant gravity and no drag. Real jumps may travel less because wind, posture, and technique change the path.
6) Why can landing height change the answer?
If the landing surface is lower than takeoff, the athlete stays in the air longer and distance increases. If landing height is higher, airtime shortens and range drops.
7) What gravity should I enter?
Use 9.81 m/s² for Earth unless you need a special scenario. Changing gravity is helpful for teaching projectile motion or testing how sensitive results are to assumptions.
8) What is the trajectory graph showing?
The graph shows horizontal distance on the x-axis and height on the y-axis. It traces the ideal jump path from takeoff to landing using your entered values.