A particle is projected with a velocity v, so that its horizontal range twice the greatest height attained. The horizontal range is

Given, a particle having horizontal range is twice the greatest height attained by it, i.e. R = 2Hv2sin2θg=2v2sin2θ2g                                               ⇒2sinθcosθ=sin2θ⇒tanθ=2⇒  sinθ=25⇒cosθ=15∴  R=v2sin2θg=v2×2sinθcosθg⇒  R=v2×2g×25×15 i.e.   R=4v25g