Projectile motion lab
Drag the barrel to set the angle and the knob to set the speed, fire, and see how far it goes. Then add air drag and find the angle that really gives the longest shot.
This interactive 3D projectile lab needs a browser with WebGL. The explanation of the model and the questions below do not.
How projectile motion works
A projectile moves under gravity alone. Its horizontal velocity stays constant while the vertical velocity changes by g every second, so the path is a parabola. Without air the range is v₀² sin 2θ / g, the same for θ and 90° − θ, and the greatest range from the ground is at 45°.
In this virtual lab you aim a launcher in 3D, pick a golf ball, baseball, cannonball or shuttlecock and fire it on Earth, the Moon or Mars, in a vacuum or in air with quadratic drag. You measure range and time with instruments that have a least count, record them in a table that exports to CSV, and compare a measured range-against-angle curve with the closed form and with the drag model.
Frequently asked questions
What launch angle gives the longest range?
From flat ground and without air, 45°. From a height the best angle is lower: tan θ = v₀ / √(v₀² + 2gh). With air drag it is also lower than 45°, typically 30° to 40° for a golf drive, because a steep shot spends more time in the air and loses more speed.
Why do 30° and 60° give the same range?
Without drag the range is v₀² sin 2θ / g and sin 2θ is the same for θ and 90° − θ. The 60° shot goes higher and stays in the air longer, but its horizontal speed is lower, so the two effects cancel exactly.
How does air resistance change the path?
Drag acts against the velocity and grows with its square, so the projectile loses range, flight time and height, and the path is no longer symmetric: the descent is steeper than the climb. Heavy, small bodies such as a cannonball are affected much less than a shuttlecock.
What is terminal velocity?
It is the speed at which drag equals weight, so a falling body stops accelerating: v = √(2mg / (ρ Cd A)). The lab shows it for the chosen body, about 44 m/s for a golf ball in sea-level air.
How accurate is this simulation?
Without drag it matches the closed form to better than one part in a million. With drag it uses fourth-order Runge-Kutta, whose result does not change when the step is halved. The physics is simplified: constant drag coefficient, no wind and no spin.