After suffering trauma to his brain, Jack experienced profound alterations in his personality. Prior to his accident he was a prudent, responsible employee. Afterward, he was childlike in mental capacity, impulsive, and unable to control his emotions. Jack's injuries were most likely located in which area of the brain

Prefrontal cortex.

Explanation:

The prefrontal cortex is an integral part of an individual's cognitive control functioning. It covers the front part of the frontal lobe, where various sensory modalities are integrated.

So, when Jack suffers the trauma to his brain, the alterations to his personality are the effects of the damage in his prefrontal cortex. Since this part of the brain is responsible for one's executive movements like focus, understanding the consequences of one's actions, personality development, decision making, etc, Jack's trauma left him devoid of these abilities.

Thus, his injury is in his brain's prefrontal cortex.