Projectile Motion Simulator
Visualize the trajectory of a projectile. Adjust angle, velocity, and height to see the path and key metrics calculated in real-time.
What is Projectile Motion?
In physics, projectile motion is the path an object takes when it's thrown or launched into the air, subject only to the force of gravity. Think of a basketball shot, a thrown baseball, or a cannonball—they all follow a curved path called a trajectory.
This simulator lets you explore how changing the initial velocity, launch angle, and height affects this path. Play with the controls below to build an intuition for the physics!
Simulation Controls
Max Height
0.00 m
Time of Flight
0.00 s
Range (Horizontal Distance)
0.00 m
How to Use the Simulator
1. Set Initial Conditions
Use the sliders to adjust the Initial Velocity, Launch Angle, and Initial Height. You can also change the value for Gravity to simulate motion on other planets!
2. Launch the Projectile
Click the "Launch" button to start the animation. Watch the projectile follow its trajectory. The path will be traced in blue, with orange dots marking each second of flight.
3. Analyze the Results
The cards below the simulation update in real-time, showing the calculated Max Height, total Time of Flight, and horizontal Range of the projectile.
Understanding Projectile Motion
What is Projectile Motion?
Projectile motion is the motion of an object thrown or projected into the air, subject only to the acceleration of gravity. The path it follows is called its trajectory. This simulation ignores air resistance for simplicity.
Independent Components of Motion
The key to solving projectile motion problems is to break the motion into two independent parts:
• Horizontal (X-axis): The velocity is constant because there is no horizontal acceleration (ignoring air resistance).
• Vertical (Y-axis): The velocity changes due to the constant downward acceleration of gravity.
The Optimal Angle
For a projectile launched and landing at the same height, the maximum range is achieved at a launch angle of 45 degrees. Angles that are complementary (add up to 90°, like 30° and 60°) will have the same range. Try it in the simulator!
Formulas in Detail
Initial Velocity Components
Position at time (t)
Time of Flight (to y=0)
Maximum Height
The 'Aha!' Moment: A Physics Student's Story
Meet Leo, a high school physics student. His homework problem is: "A basketball player shoots from 7 meters away. They release the ball at a height of 2 meters with an initial velocity of 8.5 m/s at an angle of 55 degrees. If the hoop is at a height of 3.05 meters, will the ball go in?"
Leo opens the Projectile Motion Simulator. He sets the Initial Height to 2m, Initial Velocity to 8.5 m/s, and Launch Angle to 55°. After launching, he watches the animation. The simulator calculates the full trajectory, but Leo needs to know the ball's height specifically at the 7-meter mark.
By observing the animated path and the grid, he can visually estimate that the ball is indeed near the hoop's height at that distance. The visual confirmation makes it click: the complex formulas he learned in class perfectly predict the real-world path of a basketball. He can now confidently solve the problem on paper, knowing what the answer should look like.
Frequently Asked Questions
What do the colored arrows (vectors) mean?
The arrows show the projectile's velocity components. The green vector is the constant horizontal velocity (Vx), the magenta vector is the changing vertical velocity (Vy), and the yellow vector is the total instantaneous velocity (the combination of both).
Does this simulation account for air resistance?
No, this is an idealized physics simulation. It assumes the only force acting on the projectile after launch is gravity. In the real world, air resistance would significantly affect the trajectory, especially for light objects at high speeds.
Why is the horizontal velocity (green vector) constant?
In this idealized model, there are no horizontal forces acting on the projectile after it is launched (we ignore air resistance). According to Newton's First Law, an object's velocity will not change unless a force acts on it. Therefore, the horizontal velocity remains constant throughout the flight.
How does gravity affect the projectile?
Gravity is a constant downward force, which causes a constant downward acceleration (g). This acceleration only affects the vertical velocity (magenta vector), causing it to decrease as the projectile rises, become zero at the peak, and then increase in the downward direction as the projectile falls.
What happens if I launch from a height?
Launching from an initial height (y₀ > 0) gives the projectile more time in the air. This extra flight time allows it to travel a greater horizontal distance (range) and reach a higher maximum height relative to the ground compared to a launch from y=0 with the same initial velocity and angle.
What's the difference between Range and Displacement?
Range is the total horizontal distance the projectile travels. It's a scalar quantity (just a number, like 100m). Displacement is a vector that points from the starting position to the ending position. It has both magnitude (the straight-line distance) and direction. This simulator calculates the horizontal range.
Projectile Motion in the Real World
Sports Science
Athletes and coaches use these principles to optimize performance. A quarterback throwing a football, a golfer hitting a long drive, or a basketball player shooting a free throw are all masters of projectile motion. They intuitively adjust velocity and angle to achieve the perfect range and height.
Engineering and Design
Engineers rely on projectile motion to design everything from fountains, where water arcs beautifully into a basin, to ski jumps, ensuring athletes land safely. It's also critical in designing systems like fire hoses to ensure water reaches its target effectively.
Video Games & Animation
Game developers use these exact physics equations to create realistic motion. Whether it's an arrow flying from a bow, a grenade being thrown, or a character jumping, the underlying code is simulating projectile motion to make the virtual world believable and immersive.
Ballistics and Forensics
In forensics, investigators use projectile motion to trace the trajectory of bullets or other objects at a crime scene. This helps them determine the origin of a projectile, which can be crucial evidence in solving a case. The military uses the same principles for artillery and missile guidance.