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Projectile graphs

Free notes · JEE Main Physics

Formulas

x(t)=ucos⁡θ t,y(t)=usin⁡θ t−12gt2x(t) = u\cos\theta\, t,\quad y(t) = u\sin\theta\, t - \tfrac12 gt^2

Projectile coordinates as functions of time

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°