Final answer:
The satellite's acceleration is determined by the resultant force acting on it, which is the vector sum of the forces applied by the astronauts. For the astronaut's mass calculation, divide the known force by the measured acceleration using Newton's second law. Recoil of the vehicle can be mitigated by internal force-balancing systems.
Step-by-step explanation:
The acceleration of the satellite can be found by calculating d) The resultant force acting on the satellite. This can be done by using vector addition to combine the forces exerted by the astronauts into a single net force vector. Once the net force (ΣF) is determined, the acceleration (a) of the satellite can be found using Newton's second law of motion, F = ma, where m is the mass of the satellite.
As an example, let's address part of the question: To calculate an astronaut's mass when a net external force of 50.0 N is exerted and the astronaut's acceleration is 0.893 m/s², we use the formula m = F / a. Plugging in the numbers, we get m = 50.0 N / 0.893 m/s², which calculates to approximately 56.00 kg.
When a force is exerted on the astronaut, the spacecraft experiences an equal and opposite force due to Newton's third law. This reaction force cumulatively affects the measurement of the astronaut's acceleration. To avoid this issue, one method could be using internal systems that generate equal and opposite forces within the spacecraft, so the net external force is zero, preventing the recoil of the vehicle.
Therefore answer is d) The resultant force acting on the satellite.