Projectile Motion

Step-by-step

1. Set the initial velocity and launch angle — or drag the barrel itself — then press Reset to fire.
2. Sliders re-aim the launcher but never re-fire mid-flight, so each shot is a deliberate experiment.
3. Watch the speed readout at the apex (the vertical component vanishes, the horizontal one never does) and compare the predicted range R (theory) with the landed value.
4. Load the Moon and Mars presets to see the same launch travel six times farther.

Key formulas

• $x = v_0 \cos(\theta) \cdot t$Horizontal position
• $y = v_0 \sin(\theta) \cdot t - \frac{1}{2}gt^2$Vertical position
• $R = \frac{v_0^2 \sin(2\theta)}{g}$Range
• $H = \frac{(v_0 \sin\theta)^2}{2g}$Max height

Frequently asked questions

Which angle gives the maximum range?

You can work it out this way: try angles between 30° and 60°.

What is the flight time for v₀=50 m/s at 30°?

T = 2v₀sin(θ)/g.

How does gravity on Mars (3.7 m/s²) affect the range?

Adjust the gravity slider.