A particle is projected from a point O with a velocity u in a direction making an angle α upward with the horizontal. After some time at point P, it is moving at right angle withits initial direction of projection. The time of flight from O to P is

when the body projected with initial velocity u→ by making angle a with the horizontal, then after time t, (at point P) its direction is perpendicular to u→. Magnitude of velocity at point P is given by v=ucot⁡αFor vertical motion: Initialvelocity (at point O)=usin⁡αFinal velocity (at point P)=−vcos⁡α=−ucot⁡αcos⁡αTime of flight (from point O to p) = tApplying first equation of motion v= u - gtt−ucot⁡αcos⁡α=usin⁡α−gt∴ t=usin⁡α+cot⁡αcos⁡αg =ugsin⁡αsin2⁡α+cos2⁡α=ucosec⁡αg