Physics simulation with general and simplified formula comparison
Projectile motion decomposes into two independent components:
Horizontal Motion
No acceleration (ignoring air resistance). Velocity is constant: vₓ = v₀ cos(θ)
Vertical Motion
Constant acceleration due to gravity: aᵧ = −g. This creates the parabolic path.
Deriving Time of Flight (General):
Key Insight: The simplified formula T = 2v₀ sin(θ)/g comes from setting h₀ = 0 in the quadratic, giving T = 0 or T = 2v₀ sin(θ)/g.