B

To analyze the trajectories of the particles A, B, and C given in the motion diagram, we can break down the problem as follows:
Step 1: Time of Flight
The time of flight of a projectile depends on its vertical motion. The particle that reaches the highest point (A, B, or C) takes longer to hit the ground. Observing the graph, particle B has a longer trajectory, suggesting it has the longest time of flight. This corresponds with option IV.
Step 2: Vertical Component of Velocity
The vertical component of velocity is maximum at the lowest point of the trajectory. In the given graph, particle C reaches lower before rising again. Therefore, it has the greatest vertical velocity at its lowest point. This corresponds to option III.
Step 3: Horizontal Component of Velocity
Particle A has a flatter trajectory, indicating a higher horizontal velocity; hence, it has the maximum horizontal component of velocity, corresponding to option I.
Step 4: Launch Speed
Launch speed is generally considered equal if all projectiles are launched from the same level, but given the curves, we identify that particle B, which has the longest trajectory, likely has the least launch speed overall. This corresponds to option II.
Therefore, the complete matching is: A-IV, B-III, C-I, D-II, which is option B.