Projectile Motion Trajectory Calculator

Projectile Motion Trajectory Calculator

Enter the initial velocity, launch angle, and gravitational acceleration to compute and plot the projectile's trajectory.
The key equations used are:
Time of Flight: \( t_{total} = \frac{2v_0\sin\theta}{g} \), Range: \( R = v_0\cos\theta \, t_{total} \), Maximum Height: \( H_{max} = \frac{v_0^2\sin^2\theta}{2g} \),
and the trajectory: \( x(t) = v_0\cos\theta \, t,\quad y(t) = v_0\sin\theta \, t - \frac{1}{2}gt^2 \).

* Enter initial velocity (m/s), launch angle (°), and gravitational acceleration (m/s²).

Step 1: Enter Parameters

Example: 20 m/s

Example: 45°

Example: 9.81 m/s²

Equations used:
Time of Flight: \( t_{total} = \frac{2v_0\sin\theta}{g} \)
Range: \( R = v_0\cos\theta \, t_{total} \)
Maximum Height: \( H_{max} = \frac{v_0^2\sin^2\theta}{2g} \)
Trajectory: \( x(t)=v_0\cos\theta\,t,\quad y(t)=v_0\sin\theta\,t-\frac{1}{2}gt^2 \)


Practical Example:
For an initial velocity of 20 m/s at a 45° angle and \( g=9.81 \) m/s², the time of flight is about 2.88 s, the range is about 40.8 m, and the maximum height is about 10.2 m.