An astronaut is stuck in space with no fuel for his thrusters. He is 250 m away from his ship and only has a heavy wrench in his possession. The astronaut has a mass of 85 kg and a moment of inertia about his center of mass of 5.7 kg-m2. The wrench has a mass of 10 kg and a moment of inertia about its center of mass of 0.34 kg-m2. The astronaut throws the wrench away from the ship at a linear velocity of 22 m/s and the wrench rotates about its center of mass at a rate of 3 rev/s.
(a) How long does it take the astronaut to reach his ship?
(b) How many revolutions does the astronaut make on his way back to the ship? Assume that the wrench was thrown in line with his center of mass.
(c) When he gets to the ship the astronaut can only hang on to the handle outside the entry to his ship if his total kinetic energy is less than 300 J. Can he hold on and re-enter his ship? If so, what is his total kinetic energy?