When the body is projected with velocity 'u' in the horizontal direction, expression for trajectory of projectile is given by,Â
             
Â
where,Â
'g' is acceleration de to gravity,
'x' is the horizontal distance covered by the particle,Â
'u' is the initial velocity of the particle, andÂ
'y' is the object in the vertical direction.Â
Consider an arbitrary chord AB which subtends an angle 
 with vertical. Let r be the radius of the circle. Now, the length of chord AB is given by
         
             
         
  Acceleration of mass along inclined plane is,
             
Since     
∴    
or                
  Since t is independent of 
, hence time of descend does not depend upon the choice of chord.
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