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 with its initial direction of projection. The time of flight from O to P is
u cosec αg
When body projected with initial velocity →u by making angle α with the horizontal. Then after time t, (at point P) it’s direction is perpendicular to →u
Magnitude of velocity at point P is given by v = u cot α (from sample problem no. 9)
For vertical motion : Initial velocity (at point O) =u sin α
Final velocity (at point P) =−v cos α=−u cot α cos α
Time of flight (from point O to P) = t
Applying first equation of motion v=u−gt
−u cot α cos α=u sin α−gt∴ t=u sin α+u cot α cos αg=ug sin α[sin2 α+cos2 α]=u cosec αg