Throwing a ball, kicking a football or launching a water rocket all follow parabolic paths. This calculator lets you plan and check a classroom experiment, including the position at a chosen time.
How to use the Projectile Motion Experiment Calculator
- Launch speed v₀
- Launch angle α
- Launch height h
- Time of interest t
- Gravitational acceleration g
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the launch speed, angle and height, and a time at which to see the position.
Inputs explained
| Field | What to enter |
|---|---|
| Launch speed v₀ | Units: m/s, km/h, mph, ft/s, knots, km/s |
| Launch angle α | Units: °, rad, arcmin, arcsec, mrad |
| Launch height h | Units: m, cm, mm, km, in, ft … |
| Time of interest t | Units: s, ms, min, h, days |
| Gravitational acceleration g | Units: m/s², ft/s², g, cm/s² |
What each result means
- Time of flight = ([vy] + sqrt([vy]^2 + 2×[Gravitational acceleration g]×[Launch height h]))÷[Gravitational acceleration g]
- Horizontal distance (range) = [vx]×([vy] + sqrt([vy]^2 + 2×[Gravitational acceleration g]×[Launch height h]))÷[Gravitational acceleration g]
- Maximum height = [Launch height h] + max(0, [vy])^2÷(2×[Gravitational acceleration g])
- Horizontal position at t = [vx]×[Time of interest t]
- Height at t = [Launch height h] + [vy]×[Time of interest t] – [Gravitational acceleration g]×[Time of interest t]^2÷2
- Speed at t = sqrt([vx]^2 + ([vy] – [Gravitational acceleration g]×[Time of interest t])^2)
Example values
How the main result changes when Launch speed v₀ changes and everything else stays at the example values above:
| Launch speed v₀ (m/s) | Horizontal distance (range) (m) |
|---|---|
| 4 | 2.4035 |
| 6 | 4.56 |
| 8 | 7.4545 |
| 10 | 11.1186 |
| 12 | 15.5678 |
| 16 | 26.8492 |
Formula
x = v₀cosα·t, y = h + v₀sinα·t − ½gt², range from y = 0
Worked example
Inputs — Launch speed v₀: 8 m/s; Launch angle α: 40 °; Launch height h: 1 m; Time of interest t: 0.5 s; Gravitational acceleration g: 9.80665 m/s².
Results — Time of flight = 1.2164 s; Horizontal distance (range) = 7.45453 m; Maximum height = 2.34823 m; Horizontal position at t = 3.06418 m; Height at t = 2.34532 m; Speed at t = 6.13301 m/s.
Key terms
- Projectile
- Object moving only under gravity after launch.
Frequently asked questions
What angle gives the longest range?
45° from ground level; less when launched from a height.
Does air resistance matter?
Yes for light or fast objects – this calculator ignores it.
Why is the path a parabola?
Horizontal speed is constant while gravity accelerates the ball downwards.
What if the height at t is negative?
The ball has already landed.