You have an extension glued into the trap. The nut right where the black tailpiece comes in....that can be tightened. I would first remove the nut and replace the poly washer with a rubber one..it will give better grip. Go the the hardware store and ask for a rubber 1½" slip joint washer.
Given that the pipe was installed just a tad short, if the problem persists, you can put a block of wood under the trap to hold it up!