So maybe you didn't quite finish homework 1. That's OK, turn in what you've got and it is better than a zero. So long as you're following the material, you will be fine. Keep in mind homework in total is only worth 10% of your grade, and I drop one problem set. There will be about 10 problem sets in total, so missing one whole set makes each of the others worth (1/9)*10%~1.1% of your grade. Missing (say) 2 problems out of 10 is only 20% of 1.1%, which is practically nothing.
In other words, no big deal to miss a homework set or parts of one here and there if you've got other things pressing or just don't get a few problems. The main thing is to understand the material and work the problems out/read the solutions when you get some time, because similar things will show up on the exams ... which are worth quite a bit more. HW is mainly for practice and learning, the numerical consequences for your grade are minor.