penguin
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Kinematics Simulator
projectile motion — click the canvas to set angle, or use the sliders
▶ Launch
⏸ Pause
↺ Reset
🗑 Clear Trails
click canvas to set launch angle | space = launch/pause
Time
0.00
s
Horizontal Δx
0.0
m
Vertical Δy
0.0
m
Speed
0.0
m/s
Peak Height
—
Initial Speed (v₀)
30 m/s
Launch Angle (θ)
45°
Initial Height (y₀)
0 m
Gravity (g)
9.8 m/s²
Simulation Speed
1.0×
Options
Air Resistance
Show vₓ / vᵧ
Compare Mode
💡
Did you know?
At 45° the range is maximised on flat ground.
Horizontal:
x = v₀·cos(θ)·t
Vertical:
y = y₀ + v₀·sin(θ)·t − ½g·t²
vₓ =
v₀·cos(θ)
(constant, no drag)
vᵧ =
v₀·sin(θ) − g·t
Max height:
H = y₀ + v₀²·sin²(θ) / 2g
Range:
R = v₀²·sin(2θ) / g
(y₀=0, no drag)