Question

An astronaut is working outside of the International Space Station when her propulsion system stops working....

An astronaut is working outside of the International Space Station when her propulsion system 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 Ma. This includes the astronaut, space suit, the gun, and all the metal pieces in the gun. The mass of the metal pieces is Mm. The gun shoots out the metal with a speed vr relative to the gun.

Part A: After firing the gun once, the astronaut is moving with a speed va relative to the space station. Derive an equation for the speed that the gun fires the metal objects, relative to the gun (vr). Show your work.

Note: The astronaut's speed is given relative to the space station, so we're using coordinates where the speed of the space station is zero.

Part B: If Ma= 160 kg, Mm=9.4 kg, and va= 0.90 m/s, solve for the speed vr.

Part C: What is the energy output by the gun in firing the metal object?

Part D: It turns out that there is a second metal piece in the gun. To increase her speed, the astronaut fires the gun again in the same direction she fired it the first time.

Draw a diagram illustrating the physics that can be used to determine the astronaut's speed after the second firing. Write down the momentum conservation equation that could be used to determine the velocity of the astronaut after this second firing of the gun. Again, this should be her speed relative to the space station. (You do not have to solve for a number.)

Please upvote if you have understood the solution.