Projectile Motion Simulator
Enter the initial speed, launch angle, starting height, and gravitational acceleration to calculate and chart the trajectory, range, and maximum height of projectile motion (ignoring air resistance). Try gravity on the Moon, Mars, or Jupiter, not just Earth.
Gravitational acceleration by celestial body
| Body | Gravity |
|---|---|
| Earth | 9.8 m/s² |
| Moon | 1.62 m/s² |
| Mars | 3.71 m/s² |
| Jupiter | 24.79 m/s² |
What is the Projectile Motion Simulator?
The Projectile Motion Simulator lets you enter an initial speed, launch angle, starting height, and gravitational acceleration, and instantly see the resulting parabolic trajectory plotted on a graph, assuming no air resistance. Alongside the chart, it automatically works out the time of flight, horizontal range, and maximum height, which makes it a quick way to double-check homework calculations or verify the numbers behind a physics report.
Rather than sticking to Earth's gravity, you can switch the gravitational acceleration to the Moon, Mars, or Jupiter and immediately see how dramatically the same launch speed and angle produce a completely different trajectory elsewhere in the solar system. That side-by-side comparison is designed to make an otherwise abstract number — the strength of gravity on another world — into something visual and intuitive, which is useful well beyond the classroom for anyone curious about how physics plays out away from Earth.
How to use the Projectile Motion Simulator
- Enter the initial speed Type in the speed of the object at the exact moment it is launched, measured in meters per second (m/s).
- Set the launch angle Use the slider or the number field to set the angle measured from the horizontal, from a flat 0° throw up to a straight-up 90°.
- Enter the launch height Specify how far above the ground the object starts. Leave this at 0 if it is being launched from ground level rather than from a height.
- Choose the gravitational acceleration Pick a ready-made preset for Earth, the Moon, Mars, or Jupiter, or type in a custom value if you want to model a different world or scenario entirely.
- Read off the results The trajectory graph updates immediately, and the time of flight, range, and maximum height are calculated automatically so you can compare them against your own working.
Tips for getting more out of it
- This tool models idealized motion with no air resistance. Real balls and projectiles experience drag, so their actual range is shorter than the calculated value.
- At a 45° launch angle, range is maximized for a given initial speed and gravity (assuming the launch height is 0).
- Switch the gravity preset to the Moon or Mars to see how dramatically range and time of flight change for the exact same speed and angle.
- A launch angle of 0° (horizontal launch) is useful for modeling something like throwing a ball horizontally from a height.
Ways to use the Projectile Motion Simulator
Checking physics homework
Plug in the numbers from a textbook problem and compare the simulator's time of flight and range against the answer you worked out by hand, to catch arithmetic slips before you submit.
Seeing how launch angle affects range
Keep the speed and gravity fixed and vary only the angle, and you will see for yourself, rather than just being told, that 45 degrees produces the longest range.
Comparing motion on other worlds
Switch the gravity preset to the Moon or Mars while keeping the same initial speed, and watch how much longer the object hangs in the air and how much farther it travels under weaker gravity.
Estimating trajectories in sports
Rough out the flight path of a thrown or kicked ball from an estimated launch speed and angle, which is a fun way to connect classroom physics to a basketball shot or a soccer kick.
Projectile motion glossary
- Projectile motion
- The motion of an object that is launched with some initial velocity and then moves freely under the influence of gravity alone, tracing a curved path through the air.
- Gravitational acceleration
- The rate at which an object speeds up as it falls under gravity. On Earth's surface this is approximately 9.8 m/s², but it differs on other worlds depending on their mass and radius.
- Time of flight
- The total length of time an object spends in the air, measured from the instant it is launched to the instant it lands.
- Range (horizontal range)
- The horizontal distance covered between the point where an object is launched and the point where it lands, measured along the ground.
- Parabola
- The symmetric, U-shaped curve traced out by projectile motion — mathematically identical to the graph of a quadratic function, which is why the two problems can be solved with the same tools.
- Air resistance
- The drag force exerted by the air on a moving object, which this simulator deliberately ignores; in reality it shortens the range and skews the trajectory away from a perfect parabola.
FAQ
Side Note — Galileo's discovery of the parabola
It was Galileo Galilei, in the 17th century, who first showed mathematically that an object thrown at an angle traces a parabola — the same curve as a quadratic function's graph. Before that, thinking shaped by Aristotelian physics pictured a thrown object as traveling in a straight line before abruptly falling, with no notion of treating horizontal and vertical motion as independent.
Galileo's key insight was to combine two independent motions: constant-velocity horizontal motion (since no horizontal force acts on the object) and constantly-accelerating vertical motion (due to gravity). By considering these two motions together, he derived geometrically that the resulting path must be a parabola — a forerunner of the "resolving forces and motion into components" approach that would later become central to Newtonian mechanics.
Today, this same idea behind projectile motion underlies everything from artillery ballistics to rocket launch trajectories to the physics of a ball in sports. Rocket trajectory calculations, in particular, go far beyond this simple model — accounting for air resistance, Earth's rotation (the Coriolis effect), and the changing mass of the rocket as it burns fuel.