Projectile Motion Calculator
Projectile motion describes the curved path of an object launched into the air under the influence of gravity alone (ignoring air resistance). This calculator uses the standard kinematic equations to compute the range, maximum height, time of flight, and velocity components for any launch speed, angle, and gravitational field.
The three key equations for projectile motion launched from ground level are:
- Range: R = v²sin(2θ) / g
- Maximum Height: H = v²sin²(θ) / (2g)
- Time of Flight: T = 2v·sin(θ) / g
Where v is the initial velocity, θ is the launch angle above the horizontal, and g is the acceleration due to gravity (9.81 m/s² on Earth).
Key insights:
- Maximum range occurs at 45° (when sin(2θ) = 1)
- Complementary angles (e.g., 30° and 60°) give the same range but different heights and flight times
- The horizontal velocity remains constant throughout flight (no air resistance)
- At the apex, vertical velocity is zero but horizontal velocity is unchanged
You can also explore how projectiles behave on different celestial bodies by adjusting the gravity parameter. The Moon's weaker gravity (1.62 m/s²) makes projectiles fly about 6 times farther than on Earth for the same launch conditions.