It usually takes about two hours for the pill to be absorbed, so you should be fine as far as the vomiting goes. I don't know what pill you're on, but usually if you start the pill after your period, you start on the Sunday after it starts (Sunday start method), not on Saturday. If this is the case, it takes a week to become effective. During that week, you need to use a backup method of birth control. If you started the pack only a day late, you should be fine, just use the backup like I said. You might get some breakthrough bleeding from missing one pill, though.