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

Greatest height attained h=u2sin2θ2g                                                ....(1)                              Horizontal range R=u2sin⁡2θg=2u2sin⁡θcos⁡θg---(2) Given that R=2h⇒2u2sin⁡θcos⁡θg=2u2sin2⁡θ2g⇒tan⁡θ=2 Hence sin⁡θ=25;  cos⁡θ=15; substitute these values in equation(2)R=2u2sin⁡θcos⁡θgR=2u2(25)(15)gR=4u25g