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Speed and direction at any time

Free notes · JEE Main Physics

Formulas

v=(ucos⁡θ)2+(usin⁡θ−gt)2v = \sqrt{(u\cos\theta)^2 + (u\sin\theta - gt)^2}

Speed at time t

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°