An astronaut of mass M is floating in space at a constant distance D from his spaceship when his safety line breaks. He is carrying a toolbox of mass M/2 that contains a big sledgehammer of mass M/4, for a total mass of 3M/4. He can throw the items with a speed v relative to his final speed after each item is thrown. He wants to return to the spaceship as soon as possible.
a) To attain the maximum final speed, should the astronaut throw the two items together, or should he throw them one at a time? Explain.
b) To attain the maximum speed, is it best to throw the hammer first or the toolbox first, or does the order make no difference? Explain.
c) Find the maximum speed at which the astronaut can start moving toward the spaceship.
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