An astronaut is working outside of the International Space Station when her propulsion stops working. She's floating in space, not moving relative to space station. Rather than have the rest of the crew break out the robotic arm to pick her up, she decides to use the tools at hand. The astronaut has a gun used for equipment repair that shoots metal pieces at a high speed. The mass of the astronaut and all her equipment is LaTeX: M_aM a. This includes the astronaut, space suit, the gun, and all the metal pieces in the gun. The mass of the metal pieces is LaTeX: M_mM m. The gun shoots out the metal with a speed LaTeX: v_rv r relative to the gun. Part A: Using the variables above, solve for an equation giving the speed of the astronaut after firing the gun once.