I just wanted to add if your dog is vomiting and not poohing he could have a bowel obstruction. We thought this had happened to our dog eating a penny. Today's penny's have zinc whic will eat a hole right thru their stomach.
You should really take him to the vet if this has gone on longer then a day.
Your dog hasn't been eating or drinking just today or longer?
The cat food may have upset his stomach. I would not worry about him not eating for a day but he does need fluids.
It is not unusual for dogs to vomit on occasion, however, it is not something to be ignored.
Has he been eating grass or plants? Some plants are poisonous.
Any chance he could have ingested anti-freeze? These scenarios would be considered a medical emergency and should warrant a trip to the Vet immediately.
This could be a sign of an infection.
Just no way to tell you for sure. You need to either get to a Vet if you think he may have invested something poisonous. Keep an eye on him for any other symptoms, more vomiting, not eating, lethargy, signs of pain, etc.
Hope all will be ok.