Projectile Motion Simulator – Online Launch Cannon

Projectile motion is the motion of an object thrown or launched into the air, subject only to the acceleration of gravity. The object is called a projectile, and its path is called its trajectory. In classical mechanics, a projectile's motion can be described by two independent components: horizontal motion (constant velocity) and vertical motion (uniformly accelerated by gravity). This creates the characteristic parabolic path.

On level ground (initial height = 0), the maximum range is achieved at a 45° launch angle. This is because the range formula R = v₀²sin(2θ)/g is maximized when sin(2θ) = 1, which occurs at θ = 45°. However, if the initial height is above ground level (e.g., launching from a cliff), the optimal angle decreases below 45° because the extra height provides additional flight time, favoring a more horizontal launch.

Gravity is the sole force acting on a projectile (neglecting air resistance). It causes the vertical component of velocity to decrease on the way up and increase on the way down at a rate of g = 9.81 m/s² on Earth. Lower gravity (like on the Moon: 1.62 m/s²) dramatically increases both range and flight time, while higher gravity (like Jupiter: 24.79 m/s²) shortens trajectories significantly. Use our simulator's gravity presets to compare planetary differences!

Horizontal velocity: v_x = v₀·cos(θ) (constant)
Vertical velocity: v_y = v₀·sin(θ) − g·t
Time of flight: t_f = (v₀sinθ + √(v₀²sin²θ + 2gh₀)) / g
Range: R = v₀cosθ · t_f
Maximum height: h_max = h₀ + (v₀sinθ)²/(2g)
Trajectory equation: y = h₀ + tan(θ)·x − g·x²/(2v₀²cos²θ)

Yes! In the real world, air resistance (drag) significantly alters projectile trajectories. It reduces range, lowers maximum height, and makes the descent steeper than the ascent (asymmetrical path). Our simulator models ideal vacuum conditions for educational clarity, but real-world applications like sports, ballistics, and engineering must account for drag forces which depend on speed, cross-sectional area, and air density.

Simulating projectile motion under different gravitational conditions helps students understand how gravity governs trajectory shape. On the Moon (1/6 Earth's gravity), a projectile travels about 6 times farther. This is valuable for physics education, space mission planning, and developing an intuitive understanding of gravitational physics. Try switching between Earth, Moon, and Mars presets in our simulator to see dramatic differences!