Final answer:
The astronaut's final velocity relative to the space station after pushing the satellite away is determined by the principle of conservation of momentum, taking into account the astronaut's and the microsatellite's masses, as well as their initial and final velocities.
Step-by-step explanation:
The subject of the question relates to the conservation of momentum and possibly the concept of relative velocity in the context of spaceflight and astronautics. The scenario involves the laws of physics applicable in outer space, specifically the conservation of momentum due to Newton's third law that for every action, there's an equal and opposite reaction. When the astronaut pushes the microsatellite away, the momentum before and after the event must be equal if we assume no external forces are acting on the system.
Before the push, both the astronaut and the satellite together are moving at 2.2 m/s relative to the space station. After pushing the satellite away at 0.8 m/s relative to her previous velocity, the astronaut's velocity will also change to conserve momentum. Given that the combined mass is 116 kg and they were initially moving at 2.2 m/s, the total momentum is 255.2 kg*m/s. After the astronaut pushes away the satellite:
- Astronaut's momentum = her mass * her final velocity
- Satellite's momentum = its mass * (astronaut's final velocity + relative velocity of 0.8 m/s)
Solving these equations allows for the calculation of the astronaut's final velocity. Using the conservation of momentum m1v1 + m2v2 = m1v1' + m2v2', we can determine the astronaut's new velocity relative to the space station after she has pushed the satellite away.