How long does it take for the body to absorb pills?

I have a stomach bug today and I need to take my birth control pill. I haven’t puked in a little bit and I have been taking in water so I know I can keep something down. However, I’m worried that if I take my birth control pill, I’ll just puke it back up again.

So, my question to the collective is how long does it take for the body to absorb a pill? I really don’t want to vomit up the pill and if I’m just going to, there’s no point in taking it at all today.