Final answer:
The adjective 'hooded' is the correct description for a jacket with a part that covers the head.
Step-by-step explanation:
The adjective that describes a jacket or sweatshirt that has a part covering the head is hooded. This adjective modifies the noun by providing specific information about a feature of the clothing.
In contrast, "wooly" refers to something made from wool, which is a fiber obtained from animals like sheep and is known for its warmth even when wet. An example of using these adjectives in a sentence would be: 'I wore my hooded, wooly sweater during the chilly evening.'