We discuss the effect of ram pressure on the cold clouds in the centers of cool-core galaxy clusters, and in particular, how it reduces cloud velocity and sometimes causes an offset between the cold gas and young stars. The velocities of the molecular gas in both observations and our simulations fall in the range of $100-400$ km/s, much lower than expected if they fall from a few tens of kpc ballistically. If the intra-cluster medium (ICM) is at rest, the ram pressure of the ICM only slightly reduces the velocity of the clouds. When we assume that the clouds are actually fluffier because they are co-moving with a warm-hot layer, the velocity becomes smaller. If we also consider the AGN wind in the cluster center by adding a wind profile measured from the simulation, the clouds are further slowed down at small radii, and the resulting velocities are in general agreement with the observations and simulations. Because ram pressure only affects gas but not stars, it can cause a separation between a filament and young stars that formed in the filament as they move through the ICM together. This separation has been observed in Perseus and also exists in our simulations. We show that the star-filament offset combined with line-of-sight velocity measurements can help determine the true motion of the cold gas, and thus distinguish between inflows and outflows.