An astronaut finds herself in a predicament in which she has become untethered from her shuttle. She figures that she could get back to her shuttle by throwing one of three objects she possesses in the opposite direction of the shuttle. The masses of the objects are 5.4 kg, 7.9 kg, and 10.4 kg, respectively. She is able to throw the first object with a speed of 15.00 m/s, the second with a speed of 11.8 m/s, and the third with a speed of 7.0 m/s. If the mass of the astronaut and her remaining gear is 75.0 kg, determine the final speed of the astronaut with respect to the shuttle if she were to throw each object successfully, starting with the least massive an ending with the most massiv. Assume that the speeds described are those measured in the rest frame of the astronaut.

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