Since the block is pushed onto a conveyor belt moving at 1 m/s and its initial velocity is perpendicular to the belt's velocity, the block will experience a relative motion with respect to the conveyor belt due to friction.
Given that friction is high, we can assume that the block will eventually come to rest with respect to the conveyor belt. In other words, the minimum velocity of the subsequent motion of the block with respect to the ground will be zero.
When the block comes to rest with respect to the conveyor belt, the static friction between the block and the belt balances out the external forces acting on the block. This static friction provides the necessary force to counteract the initial motion and bring the block to a stop relative to the conveyor belt.
However, it's worth noting that if the friction between the block and the conveyor belt were not high enough to bring the block to rest, the block would continue to move relative to the ground with a velocity equal to the velocity of the conveyor belt (1 m/s) in the same direction.