Projectile Motion Calculator
Calculate trajectory, range, maximum height, and time of flight for projectile motion with step-by-step solutions.
Enter initial velocity, launch angle, initial height, and gravity. Leave empty for Earth's gravity (9.8 m/s²).
Résultats
Entrez les valeurs et cliquez sur Calculer pour voir le résultat.
Theory & Formula
Projectile Motion
Projectile motion is the motion of an object thrown or projected into the air, subject only to gravity. It follows a parabolic trajectory.
Key Equations
Horizontal Motion: \(x = v_{0x}t = v_0\cos(\theta)t\)
Vertical Motion: \(y = h_0 + v_{0y}t - \frac{1}{2}gt^2\)
Range Formula: \(R = \frac{v_0^2\sin(2\theta)}{g}\) (when h₀ = 0)
Maximum Height Formula: \(h_{\text{max}} = h_0 + \frac{v_{0y}^2}{2g}\)
Optimal Angle
For maximum range with no initial height, the optimal launch angle is 45°.
Example
A projectile launched at 30° with velocity 20 m/s has horizontal velocity vₓ = 20 cos(30°) = 17.3 m/s