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Please do not give him Motrin. Motrin is ibuprofen and can be toxic to dogs. You can read about this here:
Ibuprofen can lead to ulcers, vomiting and even kidney failure. You will want to look for loss of appetite, vomiting, black stools, abdominal pain, dehydration, weakness and lethargy.
Dog's can vomit for a number of different reasons. They vomit if given an unusual (to them) treat, a change of diet can do it, if they eat too much, some vomit if they eat grass, they vomit if they don't eat sometimes, vomit if they have a throat irritation, disease can be a cause, poisoned, and various other causes. Organ failure can also lead to vomiting as well and rear leg weakness. Rear leg weakness can be from a large number of causes including a disc issue, An intervertebral disc that has slipped or ruptured up into the spinal canal causes inflammation of the spinal cord, which in severe cases causes paralyses of the rear legs. You can read about this here:
Large dog breeds sometimes suffer from a condition called degenerative myelopathy which can also cause problems with the rear legs and paralyses. You can read about this here:
Depending on the dose of Motrin given, it may be causing additional symptoms which makes it hard to determine what might be the problem. . You can give some pepcid to help with any stomach upset that might occur. Read about Pepcid dosages and usage information here:
I would make sure he has plenty of water to drink, but have to recommend you seek vet care sooner rather than waiting.