MetaJohnZilla said: 
I'm sorry for the poor picture quality but I couldn't figure out how to create a thread on mobile. My ex planted this whole sweet potato into our plastic container garden on our apartment patio. The roots that had been growing out of the top end seem to have turned into leaves and flowers??? The roots from the bottom are firmly entrenched in the soil.
Edit: We're also growing a tomato plant, two sweet pepper plants, some ginger, and a few other things in this container. It has a deep and layered soil, mostly potting soil, sand, bark, random organic detritus, and a few layers of rocks and stones and pebbles. This is my first post but I'm going to need a lot of help on this project so I will return.
You might get vines and flowers, but you won't get sweet potatoes. Sweet Potatoes require a lot of heat to produce. My uncle grew them once with the use of black plastic. He put his hand under the plastic to see how hot it was and was shocked by it. He stuck a thermometer under it and if I recall correcting, it read 140 degrees. They also need massive amounts of light. From the photo, it looks like the light is dim.
My guess is, the tomato will do the best. It will crowd out the peppers. Ginger is grown as a houseplant in many parts of the world. There are many types of ginger and it would be helpful to know which variety you are growing as they all don't have the same needs.
Oh, and, since your tub is on a balcony, it would be helpful to know where in the world you are. Balconies are subjected to seasonal changes in light, air temperatures, wind and other natural factors. At the very least, which side of the building the balcony is on would be helpful information.
