A projectile is thrown with a speed u at an angle  θ to the horizontal. The radius of curvature of its trajectory when the velocity vector of the projectile makes an angle with the horizon is

When the velocity vector makes an angle α with the horizontal, the Component of acceleration, perpendicular to velocity, i.e. the centripetal Acceleration is g  cos  α. As horizontal component of velocity remains unchanged in angular projection of projectile, hence v  cos  g=u  cos  θ          or                    v=u  cos  θcosα---(1) As, g  cos  α provides Centripetal acceleration, hence g  cos  α=v2r r=u2  cos2  θg  cos3 α  from (1)