The standard atmospheric pressure is 1ata, 2 meters = 0.002km
The pressure of water in pool = gρh = 1000 x 9.8 x 0.002 = 19.6 Pa.
The total pressure that the person would experience =19.6 + 101325(standard atmosphere) = 101344.6 Pa,
which is approximately the same as the pressure at sea level(1ata)
In conclusion, the pressure that the person would experience is not significantly different from the standard atmospheric pressure, so it is safe to travel by plane after swimming in a 2m pool.
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