Mosquitoes fly at about two kilometers per hour (1.2 mph), which sounds slow, but at their size, it's like you flying over 100 times that! They are going blindingly fast for something that small.
You can't catch them for a few reasons. One, they see you coming. Their eyes are big and round and multifaceted, so they are quite capable of seeing above and behind themselves. You can't sneak up on a mosquito easily.
Second is your hand moves slower than they fly and has more distance to cover. The mosquito doesn't need to move far to get away from your face, while your big and slow hand has to travel all the way to your head.
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