Projectile Motion Calculator

Projectile motion is 2D motion under constant gravitational acceleration. It combines horizontal motion (constant velocity) with vertical motion (constant acceleration). The path is always a parabola. Examples: thrown balls, kicked footballs, artillery shells, water fountains.

45° gives maximum range when launch and landing are at the same height, because it balances horizontal distance with time in the air. However, if launching from a height (like a hill), angles slightly less than 45° give more range. For landing below launch height, use angles less than 45°.

No! In the absence of air resistance, mass doesn't affect trajectory. A bowling ball and golf ball launched identically follow the same path and land at the same time. Acceleration due to gravity (9.8 m/s²) is independent of mass, as Galileo demonstrated.

Time of flight is total airborne time from launch to landing. Calculated as t = 2v₀sin(θ)/g for level ground. It depends only on vertical velocity component and gravity. Higher launch angles give longer flight times (more vertical motion). Doubling initial velocity doubles flight time.

Horizontal velocity is constant while vertical velocity changes linearly with time (v = v₀ + at). Position is x = v₀t (linear) and y = v₀t - ½gt² (quadratic). A quadratic relationship between x and y creates a parabola. This assumes no air resistance.

Air resistance makes trajectories asymmetric (steeper descent), reduces range and max height, and depends on mass and shape. Optimal angle becomes less than 45°. Our calculator assumes no air resistance (vacuum). For real projectiles, especially light/fast ones, air resistance is significant.