Projectile Motion & Launch Trajectory Calculator
Calculate 2D projectile motion range, maximum apex height, flight time, and launch velocity components (vx, vy) with launch elevation and gravity options.
Calculated Results
Frequently Asked Questions
What angle produces the maximum horizontal projectile range?
In a vacuum (neglecting aerodynamic drag) on level ground (y0 = 0), a launch angle of exactly 45 degrees yields the maximum possible horizontal distance. If launching from an elevated cliff (y0 > 0), the optimal angle drops slightly below 45 degrees.
What are the core kinematic equations for projectile motion?
Horizontal displacement: x(t) = v0 × cos(theta) × t. Vertical displacement: y(t) = y0 + v0 × sin(theta) × t - 0.5 × g × t^2. Horizontal velocity remains strictly constant while vertical velocity experiences constant downward acceleration -g.
How does gravity affect maximum range on the Moon vs Earth?
Lunar gravity is roughly 1/6th of Earth's (1.62 m/s² vs 9.81 m/s²). Because range is inversely proportional to gravity (R = v0^2 sin(2theta) / g), a golf ball hit on the Moon flies approximately six times farther and stays in the air six times longer.
Does projectile mass affect flight distance in vacuum?
No. According to classical Newtonian mechanics and Galileo's equivalence principle, in the absence of air drag, all objects experience identical gravitational acceleration g regardless of mass.