Projectile Motion Calculator

Comprehensive projectile motion calculator with trajectory analysis, velocity components, and position calculations at any time during flight.

Enter Parameters Get Complete Analysis

Input Parameters

Optional: Leave empty to skip position analysis

Trajectory Analysis

Enter velocity and angle values and click "Calculate Trajectory" to see complete analysis

Important Notes

Calculations assume no air resistance and constant gravity. Results are theoretical and may vary in real-world conditions with atmospheric effects.

Understanding Projectile Motion

Projectile motion describes the curved path followed by an object launched into the air, subject only to gravity. This calculator provides comprehensive analysis including trajectory parameters, velocity components, and position at any time during flight.

The calculator handles both ground-launched projectiles (h=0) and projectiles launched from elevated positions, making it suitable for various physics scenarios.

Key Physics Concepts

Motion Components

  • Horizontal Motion: Constant velocity, no acceleration
  • Vertical Motion: Accelerated motion due to gravity
  • Independence: Horizontal and vertical motions are independent

Key Parameters

  • Range: Total horizontal distance traveled
  • Maximum Height: Peak vertical position
  • Flight Time: Total time in air
  • Trajectory: Parabolic path followed

Physics Formulas Used

Maximum Height H = h + (v₀² × sin²θ) / (2 × g)
Range R = (v₀² × sin2θ) / g
Flight Time T = (v₀ × sinθ + √((v₀ × sinθ)² + 2 × g × h)) / g
Position at Time x = v₀ × cosθ × t y = h + v₀ × sinθ × t - (½) × g × t²

Velocity Components

  • Vx (horizontal): v₀ × cosθ (constant)
  • Vy (vertical): v₀ × sinθ - g × t
  • V_total: √(Vx² + Vy²)

Variable Definitions

  • v₀: Initial velocity magnitude
  • θ: Launch angle from horizontal
  • g: Gravitational acceleration
  • h: Initial height above ground
  • t: Time elapsed since launch

Example Calculations

Input Parameters Results
V: 20 m/s
θ: 45°
h: 0 m
Max Height: 10.20 m
Range: 40.82 m
Flight Time: 2.89 s
Vx/Vy: 14.14 / 14.14 m/s
V: 15 m/s
θ: 60°
h: 5 m
Max Height: 13.66 m
Range: 19.90 m
Flight Time: 3.34 s
Vx/Vy: 7.50 / 12.99 m/s

Real-World Applications

Sports & Athletics

  • • Basketball shot trajectories
  • • Golf ball flight paths
  • • Javelin throw optimization
  • • Long jump techniques

Engineering & Military

  • • Artillery trajectory calculation
  • • Rocket launch analysis
  • • Ballistic missile design
  • • Aerospace trajectory planning

This calculator provides the mathematical foundation for understanding and predicting projectile motion in all these applications.

Advanced Analysis Capabilities

This projectile motion calculator goes beyond basic trajectory calculations by providing:

  • Complete Parameter Analysis: All key trajectory parameters in one calculation
  • Velocity Component Breakdown: Separate horizontal and vertical velocity analysis
  • Time-Based Position Tracking: Calculate exact position and velocity at any time during flight
  • Elevated Launch Support: Handles projectiles launched from non-zero heights
  • Unit Flexibility: Multiple unit systems for different applications
  • Educational Value: Clear formulas and explanations for learning physics