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A rocket is fired vertically upward. At the instant it reaches an altitude of 2770 m and a speed of 288 m/s, it explodes into three equal fragments. One fragment continues to move upward with a speed of 285 m/s following the explosion. The second fragment has a speed of 372 m/s and is moving east right after the explosion.

What is the magnitude of the velocity of the third fragment?

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