🔬 Physics & Engineering

Projectile Motion Calculator

Calculate the range, maximum height, time of flight, and velocity components for projectile motion. Enter initial velocity and launch angle for complete trajectory analysis.

🎯 Projectile Trajectory Calculator
m/s
°
m
m/s²
Trajectory Results
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📖 Projectile Motion Equations

Projectile motion describes the path of an object launched into the air, subject only to gravity (ignoring air resistance). The trajectory forms a parabolic curve.

Range = (v₀² × sin(2θ)) / g
For launch and landing at the same height
Max Height = (v₀² × sin²(θ)) / (2g)
Measured from the initial height
Time of Flight = (2 × v₀ × sin(θ)) / g
Total time in the air (same-level landing)

Velocity Components

  • Horizontal (vₓ): v₀ × cos(θ) — remains constant throughout flight
  • Vertical (vᵧ): v₀ × sin(θ) − g×t — changes due to gravity

Key Insights

  • Maximum range occurs at 45° launch angle (on flat ground)
  • Complementary angles (e.g., 30° and 60°) produce the same range
  • Doubling velocity quadruples the range (range ∝ v²)