“at the drop of a hat”别理解成“在帽子掉的时候”，真实含义是不加思索地；毫不犹豫地；立即地。

【例句】
If you need help, just call on me. I can come at the drop of a hat.
如果你需要我的帮助，给我打电话，我会毫不犹豫地过来。

I don't have any vacation time yet at my new job, so I can't just travel at the drop of a hat.
我的新工作还没有任何假期，所以我不能立即去度假。