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Projectile Motion Calculator

Projectile Motion Calculator

Physics simulation with general and simplified formula comparison

Input Parameters

m/s
°
m/s²
m

Calculated Results General

Max Height
0.00
meters
Range
0.00
meters
Flight Time
0.00
seconds
Impact Speed
0.00
m/s

Formula Comparison

Note: When h₀ ≠ 0, simplified formulas (h₀ = 0) produce errors. This comparison shows the difference.
Range +0.0 m difference
Simplified: 0 m General: 0 m
Flight Time +0.0 s difference
Simplified: 0 s General: 0 s
Error from using simplified formula:
0% range error
0% time error

Velocity Components

Horizontal (vₓ) 0.00 m/s
Vertical (vᵧ) 0.00 m/s
Initial Speed 0.00 m/s
Time: 0.00s
Position: 0, 0

Time Control

t = 0.00s
0s 10s
Simplified Assumes h₀ = 0
Time of Flight
T = 2v₀ sin(θ) / g
Range
R = v₀² sin(2θ) / g
Maximum Height
H = v₀² sin²(θ) / 2g
General Works for any h₀
Time of Flight
T = [v₀ sin(θ) + √(v₀² sin²(θ) + 2gh₀)] / g
Range
R = v₀ cos(θ) × T
(where T is the general time above)
Maximum Height
H = h₀ + v₀² sin²(θ) / 2g
Position Equations
Position at time t
x(t) = v₀ cos(θ) × t
y(t) = h₀ + v₀ sin(θ) × t − ½gt²
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