Sometimes you do something or react to something with the slightest signal or urging.
The idiom at the drop of a hat basically means to do something immediately without delay.When a hat drops off your head, it falls suddenly and very quickly and that is exactly how fast you would actually do something.
So when you do something at the drop of a hat, you do it very instantly or promptly without any time for its preparation or without wasting any time.
For example, When your grandmother who is ailing needs your help, you leave all your work immediately and reach out to her without any delay. It means you are there for her at the drop of a hat.
Example 01 : John is always ready to go fishing at the drop of a hat as it is his favorite hobby.
Example 02 : William was surprised and couldn’t believe that Kelly gave such a confident speech at the drop of a hat.
Example 03 : Richard hates his job, he would quit at a drop of a hat if he didn’t have to support his family.
Example 04 : Everyone in her department avoids talking to Lisa, she is ever ready to argue and fight for no reasons at the drop of a hat.
Example 05 : During her phase of depression, Cathy would reach out to console Catherine at the drop of a hat.
Example 06 : Jessica starts crying at the drop of a hat whenever her boss shouts at her.
Example 07 :When lazy Mary woke up and saw the clock, she realized she was late, she jumped out of the bed at the drop of a hat.
Example 08 : The fire brigade reached at the drop of a hat after being alarmed about the fire that broke out in the building.
Example 09 : Every hospital has its team of resident doctors to monitor their patients and attend to them at a drop of a hat in case of an emergency.
Example 10 : The COO of the company called for an emergency meeting and expected all the employees to be there at a drop of hat as he wanted to discuss about the new policies of the company.
Example 11 : When Rachael had unexpected visitors, she had to cook a meal at the drop of a hat even though she was really tired.