Answer:
As a marketing executive of the company looking to beg an emergency leave from a HR person who is considered to be rudy, unfamiliar with me, 45+ age and also that the company is experiencing a lot of turnovers, the best way to approach the HR would be to:
1. Write an official letter to him making the intentions clear.
2. Politely ask him to consider your request even though you two are not very familiar with each other.
3. Stress the importance of the emergency and why you have to leave.