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A firework has been launched into the air and explodes into three pieces. Magically, the pieces explode in a two-dimensional plane parallel to the surface of the earth. A 25 gram piece flies off straight west at 13 m/s, a 75 gram piece flies off straight south at 23 m/s. If we knew the whole firework had a mass of 150 grams, what then is the speed and direction of the last piece?

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