A

To analyze the motion of the particles A, B, and C, we will look at each statement one by one.
Statement A: The time of flight is based on the horizontal distance traveled and the vertical drop. For trajectories of equal horizontal distance but different peak heights, the time of flight will be different. Particle A has a steeper trajectory, indicating a longer time of flight.
Statement B: The vertical component of the velocity is highest for the particle with the highest peak, which is particle A, since it reaches the greatest height, thus having the highest vertical velocity at the moment of launch.
Statement C: The horizontal component of velocity is independent of any vertical motion, and since particle C travels on a flatter path (less vertical displacement), it will maintain a higher horizontal velocity than A and B. Hence, C has the greatest horizontal velocity.
Statement D: The launch speeds are determined by the initial velocities at launch. Given their trajectories, we see that A, B, and C had different angles suggesting different initial speeds. Therefore, C has the least launch speed.

Thus, we can correlate: A-IV, B-I, C-III, D-II, leading to Option A.