Projectile Motion Simulator

Simulate projectile motion to compute range, maximum height, time of flight, and final velocity for educational use.

Initial Velocity (m/s)

Launch Angle (degrees)

Initial Height (m)

Result

Please check your inputs.

Enter the initial launch speed (in m/s) and launch angle (in degrees) into the respective input fields. Optionally adjust the initial height and gravitational acceleration (default 9.81 m/s² for Earth) to simulate different environments like the Moon. Click the 'Simulate' button to instantly compute range, maximum height, time of flight, and final velocity. View the animated trajectory plot that shows the projectile's path in real time. Copy the results or reset the inputs to try a new scenario.

📖 How to Use This Tool

Enter the initial launch speed (in m/s) and launch angle (in degrees) into the respective input fields.

Optionally adjust the initial height and gravitational acceleration (default 9.81 m/s² for Earth) to simulate different environments like the Moon.

Click the 'Simulate' button to instantly compute range, maximum height, time of flight, and final velocity.

View the animated trajectory plot that shows the projectile's path in real time.

Copy the results or reset the inputs to try a new scenario.

📝 What Is Projectile Motion Simulator?

The Projectile Motion Simulator is an interactive educational tool that calculates key parameters of a projectile's flight under gravity. By entering initial speed, launch angle, initial height, and gravity, you instantly get the range, maximum height, time of flight, and final velocity. This hands-on approach helps students and enthusiasts visualize and understand the principles of kinematics in a clear, engaging way.

Understanding projectile motion is essential in physics, engineering, and sports. It models everything from a thrown ball to a launched rocket. This simulator makes abstract equations tangible, allowing users to experiment with different parameters and see how they affect the trajectory. It bridges theory and real-world application, making learning both effective and fun.

🧮 Formula

The simulator uses the standard kinematic equations for projectile motion (ignoring air resistance):

Range: R = (v₀² sin(2θ)) / g Maximum Height: H = (v₀² sin²θ) / (2g) + h₀ Time of Flight: T = (v₀ sinθ + √(v₀² sin²θ + 2g h₀)) / g Final Velocity: v_f = √(vₓ² + vᵧ²) where vₓ = v₀ cosθ and vᵧ = v₀ sinθ − gT Here, v₀ = initial speed, θ = launch angle, g = gravity, h₀ = initial height. These equations assume a flat surface and no air drag.

💡 Tips for Best Results

✨🚀 Start with a 45° angle to maximize range on flat ground — it's the classic optimum.

✨📊 Adjust gravity to see how a projectile behaves on the Moon (1.62 m/s²) vs Earth (9.81 m/s²).

✨🔍 Use a small initial height to explore how launch elevation affects time of flight and impact speed.

✨🎯 Compare results with real-world sports like basketball or golf to connect theory to practice.

❓ Frequently Asked Questions

Can I simulate with air resistance?

This tool uses an ideal physics model neglecting air drag. For most educational purposes, that's sufficient to learn core principles. For advanced simulations, you would need to include drag forces.

What units does the simulator use?

All inputs and outputs use SI units: meters per second (m/s) for speed, meters (m) for height and range, seconds (s) for time, and m/s² for gravity. This keeps calculations consistent and easy to interpret.

Why is the range zero for a 90° angle?

At a 90° launch angle, the projectile goes straight up and then straight down, so there is no horizontal displacement. The range correctly shows zero, illustrating that all motion is vertical.