At the drop of a hat - Do it immediately without thinking about it
Origin - In the 19th century it was common to begin a race or a fight by dropping a hat or sweeping it in a rapid downward motion.
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Toe the line (conform)
Members of the British Royal Navy were required to stand barefoot and at attention for inspection. While at attention they lined up along the seams of the planks of the deck with their toes touching the line. This became known as “toeing” the line .
I think there are quite a lot of idioms that originated in the navy
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I wonder why the requirement to be bare footed?
Because slick-soled shoes were dangerous on-board ships.
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And also the ban on roller skates on board back in those days and even now 
not that they were that dangerous but because one minute you could be skating up hill and the next second downhill
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Try climbing rope rigging in leather dress shoes. Wooden decks were often waterlogged and wet, once again creating slick conditions. Bare feet for the working grades offered better conditions than footwear of the day. The officer grades would still be wearing their boots, but they also weren’t having to physically do much but shout orders. Non-skid and deck shoes wouldn’t be invented for centuries…