🎯 Projectile Motion — Interactive Physics Simulation

Explore launch angle, initial speed, range, maximum height, and time of flight. Watch how the trajectory is built from two completely independent motions acting simultaneously.

⚡ Common Misconception — and the Truth: Many students think that moving horizontally somehow changes how fast something falls, or that the horizontal speed slows down because of gravity. This simulation proves otherwise: the blue (horizontal) arrow stays exactly the same length throughout the entire flight, while the red (vertical) arrow grows steadily downward. Gravity affects only the vertical component — the two motions are completely independent.
Simulation
t = 0.00 s
H = 0.00 m
R = 0.00 m
vx = — m/s
vx = — m/s
vy = — m/s
|v| = — m/s
Horizontal velocity (vₓ — constant)
Vertical velocity (v_y — changes)
Resultant velocity
Projectile & trail
Dropped ball (same height)
Controls
v₀ — total launch speed
θ — angle above horizontal
g — try Moon (1.6) or Mars (3.7)!
y₀ — height above ground
Time
0.00
seconds
Max Height
—
metres
Range
—
metres
vₓ (horiz.)
—
m/s (constant!)
v_y (vert.)
—
m/s
Speed |v|
—
m/s
Independence of Motion — Side by Side

Each mini-view shows only one component of the projectile's motion. Notice how the horizontal position grows at a constant rate while the vertical position follows a curved (accelerated) path. Neither panel knows about the other.

🔵 Horizontal (x)
No force → constant speed → uniform motion
🔴 Vertical (y)
Gravity → increasing speed → accelerated motion
Live Graphs
x-position vs time
y-position vs time
vₓ vs time (horizontal)
v_y vs time (vertical)

The vₓ graph is a flat horizontal line (constant). The v_y graph is a straight downward slope (uniform acceleration = g). This is the independence of motion made visible.

Key Equations
Horizontal velocity
vₓ = v₀ cosθ
Vertical velocity
v_y = v₀ sinθ − g·t
Horizontal position
x = vₓ · t
Vertical position
y = y₀ + v₀sinθ·t − ½g·t²
Time of flight (y₀=0)
T = 2v₀sinθ / g
Maximum height
H = (v₀sinθ)² / (2g)
Range (y₀=0)
R = v₀² sin(2θ) / g
Speed at any time
|v| = √(vₓ²+v_y²)