Projectile Motion

Analyzing 2D motion under constant gravitational acceleration

Golden Rule: Horizontal and vertical motion are completely independent. Horizontal velocity is constant; vertical motion is free-fall at g = 9.8 m/s².

• Step 1: Define coordinates and resolve initial velocity — Choose up as +y, right as +x. If the projectile is launched at angle θ above horizontal with speed v₀, then v₀ₓ = v₀ cos θ and v₀ᵧ = v₀ sin θ. If launched horizontally, v₀ᵧ = 0.
• Step 2: Write the kinematic equations for each axis — Horizontal: aₓ = 0, so x = v₀ₓ t and vₓ = v₀ₓ (constant). Vertical: aᵧ = −g, so y = v₀ᵧ t − ½g t² and vᵧ = v₀ᵧ − g t.
• Step 3: Identify what the problem is asking — Common targets: (a) time of flight — set y = 0 and solve for t. (b) range — use t from (a) in x = v₀ₓ t. (c) max height — set vᵧ = 0 and solve for t, then substitute into y equation.
• Step 4: Solve the algebra and check units — Solve the chosen equation for the unknown. Substitute numbers with consistent units (meters, seconds, m/s). Always check that your answer is physically reasonable — range and height should be positive.