Projectile Motion Trajectory Calculator

Projectile Motion Trajectory Calculator

Calculate the projectile motion parameters using the formulas:
\( T = \frac{2v_0\sin(\theta)}{g} \), \( H = \frac{v_0^2\sin^2(\theta)}{2g} \), and \( R = \frac{v_0^2\sin(2\theta)}{g} \).
where \( v_0 \) is the initial velocity (m/s), \( \theta \) is the launch angle (degrees), and \( g \) is the gravitational acceleration (m/s²).

* Enter initial velocity, launch angle, and gravitational acceleration.

Step 1: Enter Projectile Parameters

Example: 50 m/s

Example: 45°

Default: 9.81 m/s²

Derived Formulas:
\( T = \frac{2v_0\sin(\theta)}{g} \), \( H = \frac{v_0^2\sin^2(\theta)}{2g} \), \( R = \frac{v_0^2\sin(2\theta)}{g} \),
and the trajectory equation
\( y = x\tan(\theta) – \frac{g\, x^2}{2v_0^2\cos^2(\theta)} \).


Example:
For \( v_0 = 50\,\text{m/s} \), \( \theta = 45^\circ \), and \( g = 9.81\,\text{m/s}^2 \), the calculator computes the time of flight, maximum height, and range.