📐 Projectile Motion Diagram
v₀
Initial velocity (m/s)
θ
Launch angle (degrees)
h₀
Initial height (m)
g
Gravity (m/s²)
R
Range (m)
H_max
Maximum height (m)
🧮 Enter Launch Parameters
📖 Projectile Motion Equations
v₀ₓ = v₀ cos(θ), v₀ᵧ = v₀ sin(θ)
Velocity components at launch
t_max = v₀ᵧ / g
Time to reach maximum height
H_max = h₀ + v₀ᵧ² / (2g)
Maximum height reached
t_flight = (v₀ᵧ + √(v₀ᵧ² + 2gh₀)) / g
Total time of flight
R = v₀ₓ × t_flight
Horizontal range (distance traveled)
v_impact = √(vₓ² + vᵧ²)
Impact velocity magnitude
About the Projectile Motion Calculator
This free projectile motion calculator helps physics students, engineers, and educators analyze the trajectory of objects launched into the air. Get detailed step-by-step solutions for range, maximum height, time of flight, and impact velocity.
What is Projectile Motion?
Projectile motion describes the curved path of an object thrown into the air, influenced only by gravity (ignoring air resistance). The motion can be analyzed as two independent components: horizontal (constant velocity) and vertical (accelerated by gravity).
Key Concepts
- Range: The horizontal distance traveled before landing
- Maximum Height: The highest point reached in the trajectory
- Time of Flight: Total time the projectile is in the air
- Impact Velocity: The speed at which the projectile hits the ground
- Optimal Angle: The launch angle that maximizes range (45° for level ground)
Applications
- Physics education and homework
- Sports science (baseball, football, golf trajectories)
- Engineering and ballistics
- Video game development
- Military applications
- Fireworks and pyrotechnics design
Tips for Using This Calculator
- Enter the initial velocity in meters per second (m/s)
- Specify the launch angle between 0° and 90°
- Set initial height to 0 for ground-level launches
- Use different gravity values for other planets (Moon: 1.62 m/s², Mars: 3.71 m/s²)