Projectile Motion Calculator – Trajectory Physics
Calculate trajectory, range, and flight time of projectiles
Table of Contents
How to Use
- Enter the initial velocity in m/s or ft/s
- Enter the launch angle in degrees (0-90)
- Enter the initial height above ground
- Click calculate to see trajectory results
What is Projectile Motion?
Projectile motion describes the motion of an object thrown or projected into the air, subject only to gravitational acceleration. The path followed by a projectile is called its trajectory.
Understanding projectile motion is essential in physics, engineering, sports science, and ballistics.
Kinematic Equations
Projectile motion can be analyzed by breaking velocity into horizontal (vₓ) and vertical (vᵧ) components:
- vₓ = v₀ × cos(θ) - Horizontal velocity (constant)
- vᵧ = v₀ × sin(θ) - Initial vertical velocity
- Maximum height: h = h₀ + (vᵧ²)/(2g)
- Time of flight: t = (vᵧ + √(vᵧ² + 2gh₀))/g
- Range: R = vₓ × t
Optimal Launch Angle
For maximum range on level ground, the optimal launch angle is 45 degrees. However, this changes when launching from a height or accounting for air resistance.
Applications
- Sports (basketball, golf, baseball trajectory analysis)
- Military ballistics and artillery
- Engineering (fountain design, water jets)
- Video game physics engines
- Rocket and missile trajectory planning
Frequently Asked Questions
- What is the best angle for maximum range?
- For projectiles launched and landing at the same height with no air resistance, 45 degrees gives the maximum range. When launching from a height, angles slightly less than 45 degrees are optimal.
- Does this calculator account for air resistance?
- No, this calculator assumes ideal conditions with no air resistance. In reality, air drag significantly affects projectile motion, especially at high velocities or for objects with large surface areas.
- Why does my projectile fall faster than the calculator predicts?
- Real projectiles experience air resistance, which causes them to slow down horizontally and fall faster than predicted by simple kinematic equations. The difference is more pronounced for lighter objects with larger surface areas.
- Can I use this for rocket trajectories?
- This calculator is suitable for unpowered projectiles. Rockets with continuous thrust require more complex calculations that account for changing mass and thrust over time.
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