Hey Dasha, how are you? I hope you are doing just fine! :)
I shall provide you with information on the meaning of the expression ''at the drop of a hat'':
* The idiom ''at the drop of a hat'' is considered to be an informal expression used to mean ''immediately and without hesitating''; ''on the slightest signal or urging'' (Alludes to the dropping of a hat as a signal). So, if you do something 'at the drop of a hat', you do it willingly and without hesitation.
E.g.: ''More people should sort out their own minor problems and stop calling the police at the drop of a hat''
E.g.: ''There is a myth that we are an uncaring generation, shoving our old folk into institutions at the drop of a hat''.
E.g.: ''My uncle was always ready to go fishing at the drop of a hat''.
E.g.: ''If you need help, just call on me. I can come at the drop of a hat''.
*** Note: This expression is often used to suggest that someone does not think carefully enough about their actions.
Hope that helps!!!
Should you have any further doubts, do not hesitate to contact me. I shall be pleased to help!