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Projectile motion: decomposition

Free notes · JEE Main Physics

Formulas

x=ucos⁡θ t,y=usin⁡θ t−12gt2x = u\cos\theta\, t,\quad y = u\sin\theta\, t - \tfrac{1}{2}gt^2

Projectile coordinates

Worked example

For a fixed launch speed, the horizontal range of a projectile is maximum when the launch angle is:

  1. R = v0² sin 2θ / g
  2. R is maximum when sin 2θ = 1, i.e. 2θ = 90°, so θ = 45°

Answer: 45°