A particle is projected from the ground at an angle 30o with the horizontal with an initial speed, 20 ms-1. After how much time will the velocity vector of projectile be perpendicular to the initial velocity? [in second] Take g=10ms-2

Initial velocity u=ucos⁡θi^+usin⁡θj^Velocity after time t is v=ucos⁡θi^+(usin⁡θ−gt)j^Since u and v are perpendicular to each other, therefore, u→⋅v→=0(ucos⁡θi^+usin⁡θj^)×[ucos⁡θi^+(usin⁡θ−gt)j^]=0u2cos2⁡θ+u2sin2⁡θ−usin⁡θgt=0t=ugsin⁡θ=2010×12=4s